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DYNAMOMETERS 




DYNAMOMETERS 


BY 

REV. FREDERICK JOHN JERVIS-SMITH, M.A., F.R.S. 

EDITED AND AMPLIFIED BY 

CHARLES VERNON BOYS, F.R.S. 



NEW YORK 

D. VAN NOSTRAND COMPANY 
25 PARK PLACE 

1915 









Printed in Great Britain 


EDITOR’S PREFACE 


In completing and preparing for the press the unfinished 
manuscript of the author, I have had the advantage from long 
and intimate association with him of knowing his views on the 
subject generally. Unfortunately I had not had any dis¬ 
cussion with him upon the scheme of his book, and where the 
parts succeed one another in a manner which is somewhat 
disjointed I do not know whether he intended to introduce 
paragraphs which would connect these part©. 

From his table of contents I have learned without doubt the 
order he intended to follow, and to this I have adhered faith¬ 
fully. I have occasionally made minor corrections or explana¬ 
tions where I thought them desirable, and these are not 
indicated. Additional paragraphs are indicated by square 
brackets [ ], For any faults in these the author was in no 

way responsible. I have not thought it necessary or desirable 
to abstract every printed account of a dynamometer which I 
have found, but I have described in sufficient detail some for 
which he had left blank spaces, and a number of others 
which seemed to me to be of sufficient interest. My regret 
is that I may have overlooked so many that should have been 
included. 

It has been a pleasure to me to do my best to complete this 
book; for it shows how the author from the time that he was 
acting as his father’s curate at Taunton, and while he was 
Millard Lecturer on Mechanics at Oxford, devoted himself 
consistently to the science and art of dynamometry, and in 
that time devised and constructed nearly every known type of 
instrument, in many cases being the pioneer. 


C. V. B. 









OBITUARY NOTICE 

(From the Proceedings of the Royal Society.) 

FREDERICK JOHN JERVIS-SMITH, 1848—1911. 

The Reverend Frederick John Jervis-Smith, the only 
son of the Reverend Prebendary Smith, of Taunton, was born 
at Taunton on April 2, 1848. He was educated at Pembroke 
College, Oxford. While still a boy at home he had the great 
advantage of meeting constantly William Ellis Metford, by 
whom his natural aptitude for science and mechanics was 
stimulated so that his genius, which was so marked in these 
directions, forced him at a later date to break away from the 
narrower life which his father wished him to follow. In 
obedience to this wish he entered the Church and acted for some 
years as his father’s curate and organist, becoming later Vicar 
and Patron of the living of St. John’s, Taunton. It must have 
been at this time also that with the help of Sir John Stainer he 
attained that knowledge of music and skill at the organ and 
piano that his friends so greatly admired, for a touch such as 
his could not have been acquired in later life. 

While at Taunton he followed the bent that was so strong in 
him and carried on experimental work in his own workshop, 
acquiring by various means an intimate knowledge of workshop 
practice such as the amateur rarely possesses. In 1886 he was 
invited to take charge of the Millard Engineering Laboratory 
attached to Trinity College, Oxford, and it was here that his 
best work was done. 

A good indication of the variety of Jervis-Smith’s investiga¬ 
tions may be found by reference to the Philosophical Magazine 
in the twenty years from 1882 to 1902. The subject to which 


OBITUARY NOTICE 


viii 

he devoted himself most particularly was that of work-measuring 
machines and integrators, and many of the papers are on this 
subject. Several papers refer to the measurement of the 
torsion of rotating shafts with a view to determine the power 
being transmitted, and one of his early papers describes the 
means now adopted on large steamships, where, owing to the 
engines being turbines, indicated power cannot be ascertained 
and the torsional method is the only one available. 

Other enquiries which interested him were the magnetic 
properties of metals as affected by mechanical stress or by heat ; 
electric sparks and the influence on them of flame or pressure. 
Under this heading, probably, should be mentioned his beautiful 
electrically produced images of coins that he called inducto- 
script. 

One of the most valuable results of Jervis-Smith’s ingenuity 
and mechanical aptitude is his tram chronograph. Those who 
have used the old pendulum myographs so usual in physiological 
laboratories, where the time records are rendered tiresome by 
the variable speed of the recording surface, should be the first 
to appreciate this beautiful instrument, in which trouble from 
this cause is entirely eliminated. A still greater value has been 
given to this instrument by the perfection of the electro¬ 
magnetic styles that he invented and made. By making his 
electromagnets extremely small and the yoke relatively short 
and thick he reduced the latent period, so that this chronograph 
is now not only the most convenient but the most accurate 
instrument for ballistic and other measurements of the kind. 

Other subjects of less interest perhaps in which Jervis-Smith 
made investigations or inventions were in relation to mer¬ 
cury pumps and means for raising the mercury continuously 
and automatically, quick distillation of mercury in vacuo , 
recalescence of iron, and high resistances made of graphite and 
plaster of Paris. 

During the last few years since his retirement to his charming 
house near Lymington Jervis-Smith was greatly interested in 
glowing phenomena in vacuous bulbs moved or spun in electric 


OBITUARY NOTICE 


ix 


and magnetic fields. On these he made numerous original 
experiments, but up to the present these results are not well 
understood. 

Jervis-Smith was awarded a medal at the Paris Exhibition 
of 1878 for a dynamometer, and at the Inventions Exhibition 
at South Kensington he was awarded a silver medal for his 
work on dynamometers! He also received a medal from the 
Royal Humane Society for rescuing a person in danger of being 
drowned. He was a member of the Committee on Explosives 
appointed by the Home Office in 1895—96. He became a 
Fellow of the Royal Society in 1894. 

He was keenly interested in the historical side of Physical 
Science, and often brought to light curious anticipations of 
more recent inventions. He found, for instance, that the tele¬ 
phone had been made and described in Italy as an instrument 
for recording taps upon it by movement at the receiving end. 
The former inventor had apparently invented the same instru¬ 
ment as Bell, but he never thought of speaking into it. This 
historical appreciation made the selection of Jervis-Smith to 
represent the University of Oxford at the tercentenary of 
Torricelli at Faenza in 1898 singularly appropriate. 

Throughout his career one subject was constantly receiving 
his attention, and that was dynamometry in its widest sense. 
On this he had been collecting papers all his life, and in his later 
years he was putting these in order in the hope of seeing the 
great work completed which had gained so much from his 
originality. It is hoped that this will appear this year. 

He married Annie Eyton, second daughter of T. Taylor, Esq., 
who with one surviving son remains to mourn his loss. 

The singular charm, humour, and modesty of Jervis-Smith, 
no less than his genius, made his friendship a valued possession. 
The writer of this notice found in addition a community of taste 
and a mutual sympathy, and he has lost his closest and most 
valued friend and counsellor. 


C. Y. B. 








































































CONTENTS 

PAGE 

Editor’s Preface ........ v 

Obituary Notice .vii 

CHAPTER I 

Introduction 

Importance of dynamometric tests—Ergometer—Gravity, Fric¬ 
tional and Transmission Dynamometers—Ideal gravity 
method—Smeaton : Wind-mill test—Unit of work: the inch- 
ounce—De Borda—Atwood—Watt, and Farey on Watt— 
Horse-power unit of Watt—Horse-power first mentioned— 
Sliding rule : Watt—Edgeworth : his method applied to 
modern vehicles—Poncelet on Coulomb: The work done by 
man—Work done in unloading ships—Gravity test of engine 
— Hirn : his band machine — Joule’s gravity method — 
Acknowledgment to authors and institutions ... 1 

CHAPTER II 
Friction 

The laws of friction—References to authors of researches on friction 
—Experimental determination of friction, and table of 
results—Method of least squares applied to the calculation 
of the coefficient of friction — Diagram on square ruled 
paper deduced from experimental results—[Graphic treat¬ 
ment preferable in certain cases]—[Logarithmic and semi- 
logarithmic ruled paper]—Graphic method of showing the 
value of friction between a band and a pulley. (Cotterill’s 
method)—Mechanical method of drawing the equiangular 
spiral, by the author—Coefficient of friction between band 
T 

and pulley, equation == e ^ e —[Use of Dr. Roget’s log log 

slide rule for calculating e ^ e ]—Automatic machine by the 
author for finding the friction of a belt on a pulley—Experi¬ 
ments by Imray—Experiments by the author—[Simple 
experiment with umbrella and tape]—[Use of bollard friction 
in drawing wire]—[S. G. Brown’s mechanical relay]—[Dr. J. 

G. Gray’s use of mechanical relay]—[Lateral friction] 


17 


xii 


CONTENTS 


CHAPTER III 
Planimeters 

PAGE 

The earliest application of the area method of finding the product 
of force and space : the Watt-Southern steam engine indi¬ 
cator—Recording apparatus used in conjunction with work¬ 
measuring machines—General Morin and Ernst integrator— 

Disc and roller—Ashton and Storey steam engine integrator 
—Record of work on paper band—Application of method 
by Mr. A. Denny and by Herr Frahm—Two integrators by 
the author—The area of a figure, how found—References to 
authors of papers on integrators and planimeters—Description 
of the Amsler planimeter, showing how areas are integrated 
mechanically, with Henrici’s explanation — Mechanical 
integrator by the author, applied to power-measuring 
machines—[The steam engine power integrator of Boys]— 
Example of application of the planimeter to diagram 
from model ship dynamometer, Admiralty experimental 
works .......... 44 


CHAPTER IV 
Friction Brakes 

Some early applications of coiled ropes (Horner)—Bollards and 
hawsers—Resistance due to coils of rope on a cylinder—Sir 
Christopher Wren’s “ Engin ”—The rope dynamometer brake 
—Equation for the rope brake—W. Thomson’s (Lord Kelvin) 
application of the coiled rope as a dynamometer brake— . 
Abstract of Thomson’s patent: this brake invented in 
connection with laying the Atlantic cable—Unwin’s dynamo¬ 
meter—Society of Arts motor trials, use of the rope brake 
—Modification of Thomson’s brake by Capt. Sankey—Rope 
brake at the City and Guilds Technical College, London— 
Friction brake formerly at Cooper’s Hill College, showing 
method of cooling—Dynamometers by James Thomson, 
Imray, Carpentier, Raffard, Reckenzaun, Scheibe — Block 
brake dynamometers, by Prony, Coope, Appold and Amos, 

Balk, Garrett and Sons (water-cooled brake wheel), [Griffin 
Engineering Co.]—[Alden dynamometer]—[Nicholson’s lathe 
tool dynamometer] ........ 67 


CHAPTER V 
Water Brakes 

Historical — Hirn — Perry — Reynolds — Froude—Heenan and 

Froude—Brotherhood ....... 95 


CONTENTS 


xiii 


CHAPTER VI 
Am Brakes 

page 

Walker—[Renard]—[Morgan and Wood]—[White and Poppe]— 

[Logarithmic chart of air brake]—[Observations on air brake] 113 

CHAPTER VII 

Magnetic Brake Dynamometer 

Arago’s observation—Foucault’s observation — Violle’s measure¬ 
ments— Morris and Lister . . . .. . .121 

CHAPTER VIII 
End Thrust Brakes 

Bourdon—Jervis-Smith . . . . . . . .125 


CHAPTER IX 
Historical 

Coulomb—Prony on Coulomb—De Borda—Marey—[Hele-Shaw] 

— [Froude’s lecture at the Royal Institution]—[Osborne 
Reynolds and critical velocity] . . . . .128 

CHAPTER X 

Transmission Dynamometers 

The function of this type of dynamometer—A. Morin : Translation 
from the French of his description of original dynamometers : 
Ernst’s integrator—Dynamometers of Messrs. Easton and 
Anderson — William Froude — Jervis-Smith — Dynamic 
weighing by Taring—Dynamometers of Ayrton and Perry, 

F. Von Hefner Alteneck, Matter, King, [Boys], Bourry, 
Megy, Ruddick, Valet, Neer, Latchinoff, Tatham, Farcot, 
Parsons, Saurin, Dalby, [Amsler], [Moore]—[Worm testing 
machine of Lanchester]—[Draw-bar dynamometers] . .144 

CHAPTER XI 

Torsion Power-measuring Machines or Torsion Meters 

The necessity for this kind of power measurer—Remarks by 
Mr. Archibald Denny—The principle underlying the con¬ 
struction of torsion power-measuring machines—Method 
of calculating the torsion, the transverse elasticity G 
being known—Experimental determination of G for a small 
rod .......... 190 


XIV 


CONTENTS 


CHAPTER XII 

Torsion Power-measuring Machines of Different Inventors 

page 

Him—Jervis-Smith—Mechanical and optical methods of reading 
the angle of torsion—The rotostat—Lord Rayleigh : quota¬ 
tion on this subject—Application of the rotostat for comparing 
the speed of two engines—Jervis-Smith : Another optical 
method of reading the angle of torsion, and an electrical 
method of reading the torsional angle—Mr. Archibald Denny 
on the electrical method of reading the torsional angle— 

H. Frahm’s torsion meter — The torsion meter of Dr. 
Fottinger, with efficiency and power diagrams—The Denny- 
Johnson torsion meter—The torsion meter of Hopkinson 
and Tliring — [Dr. Alfred Amsler’s torsion meter, with 
comments by H. H. Broughton]—[Fritz Lux]—[Johnson]— 
[Thurston] . ....... 195 


CHAPTER XIII 
The Cradle Dynamometer 

Jervis-Smith : Ergometer for small electromotors—The cradle 
dynamometers of C. F. Brackett and Dr. Drysdale—Marcel 
Deprez: knife edge suspension—The cradle dynamometer of 
Davis and Shaw ........ 218 


CHAPTER XIV 

Dynamometric Tests of Motor-car Engines and High Speed 
Internal Combustion Engines. 

Peculiar difficulties and necessity for flexible couplings—Use of 
calibrated dynamo—“Milling machine” supports—[Insta¬ 
bility of speed with friction brakes] — [Dr. W. Watson’s 
investigations] — [Wimperis accelerometer for brake horse¬ 
power tests of motor-car engines] . . . . . 223 

CHAPTER XV 
Ship Model Dynamometer 

Froude’s original researches—Admiralty tank and equipment at 

Haslar—List of other tanks . . . . . .236 


CHAPTER XVI 

The Aeronautic Dynamometer 

National Physical Laboratory apparatus—Vickers, Sons and 

Maxim’s apparatus 247 


ILLUSTRATIONS 


PAGE 

1. Smeaton’s Whirling Machine ..... 6 

2. Hirn’s Dynamometer, modified by the Author. . 12 

3. Diagram of Curve of Friction on Square-ruled Paper 24 

4. [Semi-Logarithmic Chart] ...... 27 

5. Professor Cotterill’s Graphic representation of the 

Friction of a Belt on a Pulley .... 29 

6. Automatic Friction Machine by the Author . . 33 

7. Graphic Representation of Naperian Logarithms . 35 

8. Regulation of Arc of Contact ..... 35 

9. [Diagram of S. G. Brown’s Mechanical Relay] . . 40 

10. The Watt-Southern Indicator ..... 45 

11. The Watt Indicator ....... 45 

12. Mechanical Integrator by the Author ... 48 

13. Area Diagram ........ 49 

14—21. The Amsler Polar Planimeter . . . 51—57 

22—24. Mechanical Integrator by the Author . 58, 59 

25—26. [Engine Power Integrator by C. V. Boys] . 61, 62 

27. Record from Model Ship Dynamometer ... 65 

28. Rope coiled on Cylinder ...... 68 

29—31. Wren’s “Engin”.70 

32. William Thomson’s Rope Dynamometer ... 74 

33. Sankey’s Dynamometer.78 

34. Dynamometer at Central Institute .... 79 

35. Dynamometer at Cooper’s Hill . . . . .81 

36. Dynamometer of James Thomson .... 82 

37—38. Dynamometer of Imray . . . . 83, 84 

39. Prony’s Brake Dynamometer.87 

40. Appold’s Brake Dynamometer.89 

41—42. [Griffin Engineering Company’s Brake Dynamo¬ 
meter] ... .... 91, 92 

43. Perry’s Liquid Friction Apparatus .... 97 

44_51. Froude’s Turbine Dynamometer . . . 100,101 

52_53. Heenan and Froude’s Dynamometer . . 109, 110 

54. Brotherhood’s Dynamometer . . . . .112 






XVI 


ILLUSTRATIONS 


PAGE 

55. Air Brake, Walker.• 113 

56. [White and Poppe Diagram].117 

57. [Logarithmic Chart of Air Brake Resistance] . • 118 
58—59. Eddy Current Brake, Morris and Lister . . 123 

60. Jervis-Smith’s End Thrust Ergometer . . . 126 

61. De Borda, Stream Lines ...... 134 

62—63. [Hele-Shaw’s Stream Lines] .... 137, 138 

64—72. Morin’s Dynamometers . . . . 148—160 

73—80. Froude’s Transmission Dynamometer . . 163—167 

8i—84. Jervis-Smith’s Transmission Dynamometer . 169, 170 

85. [Amsler’s Transmission Dynamometer] . . .182 

86. [Diagram of Moore’s Electrical Dynamometer] . . 183 

87—88. [Lanchester’s Worm-gear Testing Machine] 185—187 
89. Torsion of Shaft, Diagram ...... 191 

90—91. Dynamometers by the Author 197, 198 

92—93. Bays in Reflecting Prism ... 200 

94. Torsion Meter by Denny and Johnson . 205 

95. Torsion Meter by Fottinger ..... 209 

96. Curves of Torque . . . . . .210 

97. Efficiency Curve . . . . . . .211 

98—99. Torsion Meter by Hopkinson and Turing . . 213 

100. [Torsion Meter by Amsler] ..... 216 

101. Diagram of Cradle Dynamometer . . .218 

102. Cradle Dynamometer by the Author .... 219 

103. Zodel-Voitii Coupling. ...... 223 

104—105. [Watson Dynamometer].228 

106—108. [Wimperis Accelerometer] .... 230, 232 

109. Resistance Curve of Ship ...... 237 

110—112. Froude’s Ship Model Apparatus at Haslar. 241—243 

113—115. Aeronautical Propeller Dynamometer, National 

Physical Laboratory ..... 247 

116—119. Yickers-Maxim Whirling Machine . . 249—251 






DYNAMOMETERS 


CHAPTER I 

INTRODUCTION 


Importance of dynamometric tests . . . . . . . ^3 

Ergometer ........... g 

Gravity, Frictional and Transmission dynamometers .... 5 


Ideal gravity method 
Smeaton : Wind-mill test 
Unit of work : the inch-ounce 
De Borda . . . . 

Atwood . . . . 


Watt, and Farey on Watt ......... 8 

Horse-power unit of Watt ......... 8 

Horse-power first mentioned ......... 9 

Sliding rule : Watt .......... 9 

Edgeworth : his method applied to modern vehicles .... 9 

Poncelet on Coulomb : The work done by man ..... 10 

Work done in unloading ships . . . . . . . .11 

Gravity test of engine . . . . . . . . . .12 

Hirn : his band machine ......... 13 

Joule’s gravity method .......... 14 

Acknowledgment to authors and institutions ...... 15 


In writing this book it has been my aim to place before the 
reader an account of some of those machines which have from 
time to time been invented with a view to estimate the output 
of prime-movers, and the power absorbed by machines when 
driven by engines or motors. The subject-matter is therefore 
mainly historical. It is not my intention to describe fully the 
dynamometric methods employed in measuring ship resist¬ 
ances, by means of ship models drawn through water. Of 
late several testing tanks have been built, in England, France, 
Germany, and Japan, modelled on the original Testing Tank 
D. B 











2 


DYNAMOMETERS 


of William Froude. The subject of ship model testing has 
become so large and varied that it would be quite beyond the 
scope of this book to give a full and adequate account of this 
branch of Dynamometry. In Chapter XV. a list of ship- 
testing plants will be found, including some of the construc¬ 
tional details. As the powers employed by engineers have 
increased during no long period of time from a few to 10,000 
horse-power, machines for measuring such powers have been 
modified, and designed to give accurate results under the 
different requirements of the cases to be dealt with. It is 
interesting to observe that in one of the earliest dynamo¬ 
meters, namely that of Hirn, the method employed of 
measuring power is the same as that used in the latest form of 
steamship propeller dynamometer, the horse-power delivered 
being, in both cases, found by measuring the torsion of a 
shaft. In the description of different dynamometers I have 
added figures and diagrams, in order to make the mechanical 
constructions clear when necessary. Since Prony, Hirn, 
Morin, Thomson (Lord Kelvin), and Froude may be called 
the founders of dynamometric measurement, I have given 
descriptions of the machines of the last four from their own 
original papers, practically in full. 

The inventions of these pioneers of the subject are remark¬ 
able. Prony was the first to employ the friction set up between 
two surfaces, as a measured resistance to a pulley wheel 
rotated by a prime-mover. 

Hirn made his torsional dynamometer totalise the work 
done during a given period of time. Morin added an integrator 
to his transmission dynamometer, and also an automatic 
recording apparatus, which exhibited the work done as an 
area, generated on a moving paper band ; by this means not 
only was the total ivorlc shown, but also the way in which it 
was built up during any period of time. Thomson devised a 
brake machine in which the moment of inertia of the brake, 
namely a rope, was reduced to the least workable value, 
thereby minimising the tendency to oscillate in the brake 
itself, and rendering the dynamometer steady when running. 
To Froude is due the turbine brake, in which enormous 
resistance to rotation is obtained in a small space by the useful 
application of the vortical rotation of a liquid. 


INTRODUCTION 


3 


Some years ago I published a pamphlet in which a short 
account was given of certain forms of work-measuring machines. 
It was little more than a sketch of some experiments which 
were made in Paris in 1881, and at Taunton in a private 
laboratory, on dynamometric measurements. Since then 
more experiments on the same subject have been carried on 
by me and some of the students at the Millard Engineering 
Laboratory at Oxford (1886 to 1903). Believing that some 
portions of the work may be of interest to engineers, science 
students and others not directly engaged in the design of 
machines and engines, I have collected in the following pages 
some further accounts of dynamometric experiments and 
calculations bearing on the subject, so that the reader may be 
able to compare the different methods which have been 
employed by investigators of eminence in estimating the output 
and efficiency of prime-movers and mechanical combinations 
of many different kinds. Now that a certain class of machinery, 
including the dynamo, the electric motor, and many kinds of 
engines, employed in ships and launches, railways, trams, 
motor cars, and flying machines, has undergone rapid develop¬ 
ment, and in some cases reached a high degree of perfection, 
it has become necessary that some adequate method of testing 
the comparative merits of such machines should be in the 
hands of those who make them and use them. 

One of the leading features of excellence of machinery, 
either of prime-movers or machines driven by them, is economy 
of working, so that accurate dynamometric tests of such 
machines is of paramount importance. 

An observation made by John Penn, the celebrated marine 
engineer, chairman of the Institution of Mechanical Engineers, 
in 1858, at the close of a paper by William Froude on dynamo¬ 
meters, is interesting in connection with my subject. It is as 
follows :—“ He ” (Mr. Penn) “ thought there could not be too 
many dynamometers, as they were of such importance.” 
Penn’s words were spoken at a time when the available methods 
for measuring efficiency were quite few and not much known ; 
he evidently felt that progress in the construction of the steam 
engine could be best gauged by dynamometric measurements 
of work. The masterly experiments of the late W. Froude, 
F.R.S., on the power absorbed by marine engines, and ship 

B 2 


4 


DYNAMOMETERS 


resistance, decided certain dynamometrical questions so per¬ 
fectly that the importance of this class of measurement was 
thrust with great force upon naval architects and the builders 
of marine engines. Dynamometric tests bearing on the 
structure of our battleships are now carried on daily at the 
Admiralty experimental works at Haslar under the direction 
of Mr. E. Froude, F.R.S., and similar testing plants have been 
laid down by shipbuilders who wish to conduct their own 
testing. [These have been added to recently by the con¬ 
struction of a tank at the National Physical Laboratory at 
Bushy.] Some few makers of electrical machines long ago 
(1881) realised the importance of dynamometric tests ; also 
excellent tests of this kind were made from time to time 
under the supervision of the Royal Agricultural Society of 
England. In 1888-89 the Society of Arts conducted exhaus¬ 
tive trials of motors for electric lighting. At Messrs. Willans 
and Robinson’s Engineering Works, Rugby, a complete 
department for engine testing has been arranged by 
Captain Riall Sankey and Mr. C. H. Wingfield. In a well- 
illustrated paper by Mr. W. W. Beaumont,* will be found 
detailed descriptions of dynamometers of the friction-brake 
type. My own observations from having visited many 
engineering works and technical colleges, both in England and 
in the colonies of Australia and New Zealand, lead me to believe 
that much has yet to be done in this most interesting and 
necessary branch of experimental work. The dynamometric 
test either of a prime-mover such as a steam or gas engine, 
or of a driven machine such as a dynamo or spinning loom, 
should form a definite part of the workshop procedure of 
the mechanical and the electrical engineer, since such tests 
would definitely show progress or the reverse in the machine 
produced in the works. 

It has been customary with engineers to call the machine 
used for measuring work a dynamometer. The name does 
not seem to have been well chosen, since the word, derived as 
it is from the Greek Bvvapis = force, and ^erpov = a measure, 
would imply that only force was measured, whereas work, 
i.e., the product of force into the space through which it acts, 
is measured by the machine. Since this is the case, a word 

* Proceedings of the Institution of Civil Engineers, Yol. XCV., November, 1888. 


INTRODUCTION 


5 


compounded of the Greek words epyov = a work, and j uerpov 
— a measure, would be preferable. Machines whereby work 
is measured have been called ergometers (see “ Elements of 
Natural Philosophy,” Thompson and Tait, p. 134, Part I., 
2nd ed., 1879). But as the word “ dynamometer ” has been 
so universally employed and applied to work-measuring 
machines it will be adhered to in this book. Dynamometers 
may be divided into three classes, the gravity, the frictional 
(including absorption machines), and the transmission forms. 
These and some of the methods used for obtaining numerical 
results will be considered in order. 

If we wished to measure the work done by any engine, 
whether driven by water, steam, gas, electricity, or any other 
agent, we could make such a measurement by causing the 
engine or motor to wind up a known weight from a deep shaft 
in the earth ; then the height in feet through which the weight 
is raised, at a uniform velocity, multiplied by the numerical 
value of the total weight in pounds raised would give the 
numerical value of work done in raising the load in foot-pounds. 
In order that this very simple method might be practically 
employed the winding-rope should be continuous, so that the 
rope in itself may be in equilibrium. If an unbalanced rope 
were employed, its weight must be known ; then the product 
of the height through which its centre of gravity is raised 
multiplied by its weight = the work done in raising the rope. 
The sum of the two products equals the whole work done. 

Probably the earliest instance of carefully-conducted experi¬ 
ments on the determination of the work done by a machine in 
a certain time is due to John Smeaton, E.R.S. I give two 
instances of his methods of measuring work. 

The vanes of a small windmill were carried on an axle 
mounted on an arm FG (Fig. 1) perpendicular to its length, 
the arm being capable of rotation in a horizontal plane, on 
the axle DE, mounted on the frame ABC. By means of a cord 
ZH coiled on the vertical axle, the little windmill was driven 
through the air at any required velocity ; while the windmill 
was thus impelled against the air it raised known weights P 
placed in a pan ST to a known height by means of pulleys and 
a cord MNO. Smeaton’s experiments were made on wind¬ 
mills furnished with vanes varying in shape and angular set. 


6 


DYNAMOMETERS 


A comparison between the values of the weights raised in 
different cases indicated the relative values of the different 





4 




forms of vanes and their angular set. A pendulum VX was 
used to show the time in which work was done. In another 














INTRODUCTION 


7 


set of experiments Smeaton employed a somewhat similar 
method to determine the work done in generating angular 
velocity in a certain given mass, starting from rest when 
impelled by a force acting through a given space, whereby he 
essayed to find the relationship existing between rotating 
bodies and a falling weight which propelled them. Here we 
see probably for the first time work expressed as a product. 
Smeaton writes thus : “ And this mechanic power we shall 
express by the number 202, the product of ounces in the scale 
multiplied by the inches in its perpendicular descent, for 
8 x 25J = 202 ”—about T06 foot-pounds. Smeaton’s unit of 
work was the inch-ounce, a product like the foot-pound now 
used by the modern engineer. It will be noted that Smeaton, 
by means of his pendulum, determined the time also in which 
work was done ; so that the rate of doing work , that is power, 
was found by him. In these days of aeroplane flights the 
earliest definite research in windmill sails should be of interest 
to those who are working on the behaviour of air screw pro¬ 
pellers. It will be seen in what follows that Smeaton’s 
excellent method has recently been developed into elaborate 
machines for testing the power of aerial propellers (Chap. XVI.). 

Some excellent experiments were made by M. Le Chevalier 
De Borda on the horizontal impulse wheel by means of the 
gravity method (“ Memoire sur les Roues Hydraulique,” 
par M. le Chevalier De Borda, Hist, de 1’Acad. Royal des 
Sciences, 1767). The water struck the vanes or curved blades 
of the wheel at an angle to the vertical; De Borda caused the 
hydraulic wheel to raise a weight by means of a pulley and a 
cord wrapped on the axle of the wheel, and by this means 
determined the condition of the maximum efficiency. 

Atwood, the inventor of the well-known machine which 
bears his name, when writing on the dynamics of rotating 
bodies (1784), gives an illustration of Smeaton’s instrument, 
but in his calculations the kinetic energy of the driving mass 
is included in the reckoning, and also other important points 
(“A Treatise on the Rectilinear Motion and Rotation of 
Bodies,” G. Atwood, M.A., F.R.S., Cambridge, 1784). An 
experiment involving the same dynamic condition is described 
in “ Applied Mechanics,” by Prof. John Perry, F.R.S., ed. of 
1897, p. 247. 


8 


DYNAMOMETERS 


Soon after the steam engine of James Watt had shown 
itself to be an excellent prime-mover and the horse began to be 
replaced by it, the need of some method for determining the 
comparative power of the steam engine and the horse was felt. 

The following quotation from John Farey shows clearly 
how the early estimates of horse-power were arrived at 
and determined. The passage is important historically, and 
therefore I give it at full length. 

Estimation of the Force of Steam Engines by Horse-power, 
1784 (“ The Steam Engine,” by John Farey: London, 
1827) :-— 

“ The only unequivocal mode of expressing the mechanical power 
exerted by an engine or by an animal is the weight which can be raised 
through a certain space in a given time by that exertion; and unless 
we define what a horse-power is in those terms, it is a very vague 
expression, on account of various degrees of strength which different 
horses possess, and their capacity of enduring fatigue.” 

“ When Messrs. Boulton and Watt first began to introduce their 
rotative steam engines into manufactories, about 1784, they found it 
necessary to adopt some measure of the power which they were required 
to exert; this they endeavoured to do in such terms as would be readily 
understood by the persons who were likely to want such engines. The 
machinery in the great breweries and distilleries in London was then 
moved by the strength of horses, and the proprietors of those establish¬ 
ments, who were the first to require Mr. Watt’s engines, always inquired 
what number of horses an intended engine would be equal to. 

“ In consequence, Mr. Watt made some experiments on the strong 
horses employed by the brewers in London, and found that a horse of 
that kind, walking at the rate of two and a half miles per hour, could 
draw 150 lb. avoirdupois, by means of a rope passing over a pulley, so 
as to raise up that weight, with vertical motion, at the rate of 220 ft. 
per minute. 

“ This exertion of mechanical power is equal to 33,000 pounds (or 
528 cubic ft. of water) raised vertically through a space of one foot in one 
minute, and he denominated it a horse-power, to serve for a measure of 
the power exerted by his steam-engines ; that is, of the resistance 
actually overcome, in addition to the friction of the engine itself, and 
the resistance of the air pump. . . . Messrs. Boulton and Watt’s standard 
for the horse-power is very much beyond the actual power of any horse, 
except the very strongest, and they cannot long endure the exertion of 
raising 33,000 lb. at the rate of 1 ft. per minute. Mr. Smeaton and other 


INTRODUCTION 


9 


engineers made many observations on the work actually performed by 
horses when working regularly in mills, and the results seem to show 
that 22,000 lb., raised at the rate of 1 ft. per minute, may be taken for a 
real horse-power, or as the exertion that a good horse can overcome with 
so much ease as to continue work for eight hours per day.” 

It may be noted that the first mention of horse-power in 
print occurs in Vol. II. of the first edition of the “ Mechanics ” 
of Olinthus Gregory, 1805. 

Farey was a friend of James Watt, and a man of much 
ability, and moreover the inventor of an excellent form of 
slide rule, which appears to have been much used in the cal¬ 
culation of the dimensions of Watt’s engines. Some of the 
slide rules were devised by Watt himself and one of his en¬ 
gineers, by name Southern. These instruments were known as 
the Soho sliding rule, and formed one of the everyday tools of 
the workmen employed by Watt (pp. 531—532 idem), as is 
evident from the following words :—“ and having observed 
the facility with which the Soho workmen performed their 
ordinary calculations by it.” I mention this, as I have heard 
some engineers speak of the slide rule as a new sort of instru¬ 
ment, and therefore one to be avoided. As a matter of fact 
the slide rule dates from a much earlier period, probably 1662 
(see Nature, Vol. LXXXII.). 

Experiments were made with much care by R. L. 
Edgeworth, F.R.S., on the relative work required to pull 
carriages of varied construction along ordinary roads. The 
results are collected in a volume entitled “ An Essay on the 
Construction of Road Carriages,” by R. L. Edgeworth, 1813. 
One experiment whereby the pull on two carriages carrying 
different loads was found deserves especial notice. The two 
carriages to be compared were pulled along a road by means 
of a rope attached to each, which passed round a horizontal 
pulley, the axle of which was fixed to another carriage in front, 
pulled by a horse. When the friction of each carriage was the 
same in value they advanced side by side, but when different, 
by loading, the friction of one of them was changed, one 
advanced on the other as both were pulled along (ibid., p. 191). 
Two carts, one of wdiich was furnished with springs, were 
tested ; while the load of the cart having springs was as 15 to 12, 
the carts remained abreast of one another, thus showing the 


10 


DYNAMOMETERS 


advantage of the introduction of springs. The results are 
brought together in a paper by Mr. Ward, in the Third Report 
for 1809 of the House of Commons Committee upon Road 
Wheels and Roads. 

A somewhat similar method has been used for comparing the 
friction of two boats drawn through still water, but in this 
case the relative friction was found by knowing the lengths 
of the arms of a lever, which took the place of the pulley in 
the former experiment. The author has also employed a 
modification of the same method, in which the horizontal 
wheel in Edgeworth’s experiment was furnished with a Salter’s 
balance, which indicated the difference of pull on the two 
bodies drawn along by the front carriage ; in this way the 
relative resistance of two motor cars may be easily estimated— 
the two cars under comparison not using their own engines 
during the experiment. In many other experiments the 
same method of reading the difference of pull has been 
found to give excellent results—for example, in testing the 
surface friction between two pairs of similar surfaces, in 
one set the rubber moving in a straight line, in the other 
the rubber having in addition a small simultaneous lateral 
movement. 

Coulomb investigated with great care the conditions under 
which men best performed work (Memoires de l’lnstitut 
National des Sciences et Artes : Coulomb, “ Science, Math, 
et Phys.,” T. II.). His work is commented on by Poncelet 
in his “ Mecanique industrielle ” : Paris, 1841, p. 237. The 
table exhibited by Poncelet, taken from the results of Coulomb, 
is most instructive, as it is a summary of his experiments, 
made with great care and extending over many years of 
observation. The following translation describes one of the 
most remarkable discoveries of Coulomb :— 

“ Concerning the best method for utilising the strength of man, the 
table shows that the greatest amount of work which a man can yield per 
day without undue fatigue consists in raising his own body, and this 
equals 280,800 kilogram-metre units of work in eight hours. Since the 
kilogram-metre = 7-233 foot-pounds, 280,800 kilograms = 2,031,026 
foot-pounds in eight hours, or 4,231-2 foot-pounds per minute, so that 
the rate of doing work was 0-128 horse-power—a result at least seven 
times that of a simple worker with a shovel, and one which surpasses by 


INTRODUCTION 


11 


nearly two-thirds that of a workman employed in turning a winch 
handle. In order to utilise that amount of work at disposal there is no 
question, as Coulomb observes, but to make use of the descent of the 
weight of the man in raising a weight equal to his own to the height 
which he reaches each time, i.«., each journey. Amongst the con¬ 
trivances devised to fulfil this end the most simple, and that which has 
been practically used by Captain Coignet in the construction of the 
earthworks of the fort of Vincennes, near Paris, consisted of a rope 
passing over a pulley, furnished at its ends with boards, one of which 
carried the man and the other the weight to be raised. These opera¬ 
tions, in which each workman raised the weight of his own body (70 
kilograms) 310 times daily to the height of 13 metres, have been 
thoroughly authenticated.” 

The process will perhaps be better understood if we imagine 
a grooved pulley, running on a horizontal axle fixed at the top 
of a building, furnished with a rope having its lower end 
attached to the load to be raised. The workman ascended 
the building by steps, and wdien at the top he seated himself 
on a board attached to an upper portion of the rope, the 
load being a little less than the weight of the man ; he then 
descended, regulating the rate of descent as he pleased, by 
handling the rising portion of the rope (which would be itself 
in equilibrium if continuous) until he reached the ground. 
Before he left his seat the load at the top would be removed, 
another man would take its place, and the man below who 
had made the descent would be replaced by the next load, 
which would ascend in the same manner. At the same time 
the first man would be walking up again to the top of the 
building, to be ready for the next load. 

To-day one may see ships and colliers unloaded by men 
employing the same principle as that just described. A basket 
filled with coal by men in the hold of a collier is hauled up by 
means of a rope passing over a pulley suspended from a spar ; 
the rope is furnished with numerous ends, four or five ; each 
end is seized by one of a group of men standing on a platform. 
The men jump from the platform at the same moment, and 
their joint weight brings up the load : this is then upset down 
a shoot into a lighter or truck ; the men then return to the 
platform for their next load. It is difficult to determine 
the date of this method of employing manual labour, but 


12 


DYNAMOMETERS 



it is probably a very early 
one. 

A very simple and not to 
be despised method of test¬ 
ing a prime-mover such as 
a gas engine or steam engine 
(the ports being open to the 
air) with a view to finding its 
internal friction is to set the 
engine in motion by means 
of a rope coiled on the fly¬ 
wheel, the rope being fur¬ 
nished with a weight sufficient 
to give the flywheel some con¬ 
venient slow rotation. The 
weight may either descend 
into a dry pit, or, if high 
buildings are available, the 
rope may be taken over a 
pulley at such a height that 
the weight may have the 
required fall while rotating 
the flywheel of the engine 
slowly. 

The method, which will be 
found instructive, can be 
easily applied for testing any 
small machine in which rota¬ 
tion takes place. The weight 
can be most conveniently 
applied and increased by 
means of an open cylinder 
or bucket attached to the 
cord, into which dry sand 
p IG . 2 . poured from a hopper 

furnished with a sliding gate, 
by means of which the sand can be shut off at any 
instant. It is convenient to determine the weight of the 
cylinder, so that only the sand has to be weighed in each 
experiment. 













INTRODUCTION 


13 


The machine described by Him * appears to be the proto¬ 
type of those work-measuring machines in which lines, ropes, 
or driving bands are employed in driving the machine or 
element of a machine to be tested. Two grooved pulleys are 
free to revolve on their horizontal axes, which are either in 
the same straight line or are parallel to one another. A 
continuous cord embraces half of each of the pulleys, and 
the two portions which hang down pass round pulleys, to the 
blocks of which scale pans are attached, which can be loaded 
as required. If one of the pulleys first mentioned be held 
fast, while the other is rotated, then one of the weighted pans 
will be raised and the other lowered. If one of the pulleys 
is connected to a fan, for example, the air resistance of which 
is sought, then when it is driven through the cord its tension 
is measured by hah the difference of the weights in the scale 
pans, and the work done is deduced from the velocity of 
rotation and the tension of the cord. In Fig. 2 is shown a 
modification of this apparatus by the author, the two pans 
and weights in the apparatus of Hirn having being replaced by 
a pulley carrying a loaded arm G. 

The pulleys A and B are fixed on the same axis, which runs 
on ball-bearings, A being driven by the prime-mover. The 
continuous band BDCE passes round the pulleys. The 
object to be driven, such as a wind vane, is fixed at H to the 
axis of C. To the sheaves of the pulleys D, E, a band is 
attached which passes round the pulley F and is fixed to it, 
so that when D and E are displaced the weight G, carried 
on an arm fixed to F, is raised, and from its position on a 
calibrated dial the difference of tension on the two sides of 
the driving band is known. This form of apparatus runs 
very steadily and is remarkably free from vibration. It has 
been found that good, strong fishing-line, carefully joined with 
a long splice, makes an excellent driving band when moderately 
small forces have to be dealt with. Line of this kind is largely 
employed in the Admiralty experimental ship model tank, 
and its excellence as a transmitter of motion has been con¬ 
stantly proved during a period of over fifty years that it has 

* Bulletins de la Societe industrielle de Mulhouse, 1854; and “ Recherches 
Exp^riraentales sur la Relation qui Existe entre la Resistance de l’Air et sa Tem¬ 
perature,” par G. A. Hirn, Acad. Royale de Belgique, 2 Juillet, 1881. 


14 


DYNAMOMETERS 


been employed elsewhere in connection with model ship- 
testing apparatus. 

In dynamometers of the above-mentioned type it has been 
suggested that there is some difficulty in calibrating the 
machine, arising from the idea that the effective diameter of 
a V-grooved pulley carrying the cord could not be truly 
determined. Such a measurement may be difficult to make, 
but it is not really required. What must be known is the work 
done due to the difference of the tensions on the two sides 
of the driving cord, or band, multiplied by the space through 
which this difference of the tensions acts. If while a known 
weight is raised at a uniform velocity the difference of the 
scale-pan loads, or the reading of the pointer' in the author’s 
form of this machine, be known, then the constant of the 
ergometer can be found at once. Let this difference of the 
loads or the pointer’s movement be automatically marked on 
a drum covered with paper, rotating at a speed proportional 
to the distance through which the force acts, then the area of 
such a diagram, multiplied by a suitable constant, shows the 
whole work done. For an illustration of this method see 
chapter on Planimeters. 

Before leaving the gravity method a modification of its 
application must be considered, namely, that in which a 
weight falling through a known height is made to do work. 
In the hands of Joule the gravity method of measuring work 
was turned to admirable account in his determination of the 
mechanical equivalent of heat.* The paper was read before 
the Royal Society on June 21, 1849, but before that date 
weights falling through a measured height while rotating a 
bar of iron under magnetic influence were used by Joule to 
determine the work done in heating the bar. He states the 
result obtained thus :—“ Therefore the heat evolved by a 
revolving bar of iron is proportional to the square of the mag¬ 
netic influence to which it is exposed.” A vertical axle, by 
which the iron bar was rotated, was driven by means of a 
double strand of fine twine carried over two easily-working 
pulleys placed on opposite sides of the axle. By means of 
weights placed in the scales attached to the end of the strings 

* The Scientific Papers of James Prescott Joule, F.R.S., published by the 
Physical Society of London, 1884. See ibid., p. 150, and p. 298. 


INTRODUCTION 


15 


the force necessary to move the apparatus was easily ascer¬ 
tained. In the research on the mechanical equivalent of heat, 
the same method of driving a vertical spindle connected to 
paddles by means of which water was churned in a copper 
vessel and thereby heated was employed, the fall being 63 inches 
and the weights either 29 pounds or 10 pounds a-piece. In 
order to obtain sufficient work for churning the water the 
weights were repeatedly raised, and allowed to fall, through the 
same height. The sum of all the heights of fall multiplied 
by the weights equalled the whole work done in any experi¬ 
ment in which a given weight of water was heated. The 
following correction was made : the weights reached the ground 
with a velocity of 2-42 inches per second. This was due to 
a height of 0-0076 inch and was subtracted from the fall 
in each case, giving the correct dynamic height fallen 
through. 

The author is indebted to the following gentlemen for their 
kindness in sending him original papers, drawings, and auto¬ 
matic records of work-measuring machines, and he wishes here 
to thank them for their excellent assistance. 

He also wishes to thank those institutions and societies 
which, through their several secretaries, have given him per¬ 
mission to reproduce paragraphs and figures from their trans¬ 
actions and papers. 

Sir Robert Ball, F.R.S.—Reproduction of paragraphs from 
“ Experimental Mechanics,” by permission of Messrs. Macmillan 
& Co. 

W. Worby Beaumont, M.I.C.E.—Reproduction of illustra¬ 
tions from a paper on “ Friction Brake Dynamometers,” 
Proceedings of the Institution of Civil Engineers, Vol. XCV., 
1888-89, Part I., by permission of the Institution of Civil 
Engineers, per their secretary, J. H. T. Tudsbery. 

Messrs. Blohm and Voss, Hamburg.—Drawings and full 
details of the Frahm Torsion Meter. 

G. J. Churchward.—Dynamometer Car, Great Western 
Railway Co., Swindon. 

Archibald Denny, vice-president, The Institution of Naval 
Architects. — Traces from the Denny-Edgecombe Torsion 
Meter ; “ Torsion Meters as applied to the Measurement of 
Power in Turbines and Reciprocating Engines,” 1907, by 


16 


DYNAMOMETERS 


permission of the secretary, Institution of Naval Architects, 
R. W. Dana. 

The North-East Coast Institution of Engineers and Ship¬ 
builders.—Extracts from Mr. Gibson’s paper on “ Torsion 
Meters,” by permission of the secretary, J. Duckitt. 

Engineering .—Permission to reproduce diagrams in issue of 
April 17, 1903, per the editor. 

Encyclopaedia Britannica, 10th ed., Vol. XXX.—Permission 
to reproduce matter on the subject of “ Integrators,” per the 
editor. 

Froude, E. R., F.R.S.—Traces from Tank Dynamometer 
Tests of Ship Models. 

Froude, W., F.R.S. (the late).—Permission to reproduce 
diagrams and matter from a paper by the late W. Froude, 
Proceedings of the Institution of Mechanical Engineers, per 
the secretary. 

Hopkinson, Professor B., Cambridge.—Torsion Meter for 
Propeller Shafts. 

Messrs. Taylor and Francis.—Permission to make cliches 
of original papers by the author, and reproduce the prints 
from them. 

Thompson, S. P., F.R.S.—Description of early dynamo¬ 
meters by the author in “ Dynamo-Electric Machinery,” 1884, 
page 383. 

Institution of Civil Engineers.—Permission to use illustra¬ 
tions, per the secretary, J. H. T. Tudsbery. 

W. G. Walker & Co.—Electros for figures. 

Messrs. Longmans, Green & Co.—Permission to reproduce 
figures, etc., from Willis’s “ Principles of Mechanism.” 


CHAPTER II 


FRICTION 


The laws of Friction ......... 

References to authors of researches on Friction .... 

The experimental determination of Friction, and table of results 

The method of least squares applied to the calculation of the coefficient of 
Friction........... 

Diagram on square-ruled paper deduced from experimental results 
[Graphic treatment preferable in certain cases] 

[Logarithmic and semi-logarithmic ruled paper] .... 

Graphic method of showing the value of Friction between a band and a 
pulley. (Cotterill’s method) ....... 

Mechanical method of drawing the equiangular spiral, by the author 


T 

equation 7 =^ =e^ 9 

I2 


Coefficient of Friction between band and pulley 

[Use of Dr. Roget’s log log slide rule for calculating cm#] 

Automatic machine by the author for finding the coefficient of Friction of a 
belt on a pulley .... 

Experiments by Imray .... 

Experiments by the author . 

[Simple experiment with umbrella and tape] 

[Use of bollard friction in drawing wire] 

[S. G. Brown’s mechanical relay] 

[Dr. J. G-. Gray’s use of mechanical relay] 

[Lateral Friction] ..... 


PAGE 

17 

17 

19 

21 

23 

25 

26 

28 

30 

30 

32 

32 

34 

37 

38 

39 

40 

40 

41 


Since in work-measuring machines of the absorption kind, 
in which energy received by the machines is converted into 
heat by means of friction set up between rubbing elements, 
either solid, as in the band ergometer, or liquid, as in the 
machine of the late W. Froucle, F.R.S., the laws of friction 
and certain aspects of its application demand our attention. 
It is not my purpose to give here more than a sketch of the 
subject; for exhaustive information respecting friction the 
following authors * may be consulted. 

* Coulomb, Memoir by, 1785 ; Rennie, Phil., Trans. Royal Soc , 1829 ; Morin, 
Memoir, French Acad., 1831-34 ; “ Nouvelles Experiences, etc., Faites, a Metz, 

D. 0 








18 


DYNAMOMETERS 


Up to the year 1870 the doctrine taught respecting friction 
was embodied in three laws, namely :— 

(1) The magnitude of the frictional resistance between a 
given pair of surfaces of any materials is proportional to the 
pressure that keeps them in contact. 

(2) The frictional resistance is unaffected by the area of 
contact. 

(3) The frictional resistance is wholly unaffected by the 
relative velocity of the rubbing surfaces. Subsequent research 
has shown that the third law, as given by Willis in his “ Prin¬ 
ciples of Mechanism,” is not borne out by experiment when 
applied to journals running in bearings at velocities varying 
between wide limits. 

We are greatly indebted to Hirn, Beauchamp Tower, 
Thurston, and 0. Reynolds for their exhaustive researches on 
the friction between pairs of elements moving over one another 
at different velocities. 

For the laws of friction due to a surface moving in water 
we are indebted to the late W. Froude, F.R.S. (“ The Funda¬ 
mental Principles of the Resistance of Ships,” Proceedings of 
the Royal Institution, London, May 12, 1876). See page 139. 

A statement of the laws of friction, as now received, between 
solids and a comparison of these laws with those of fluid 
friction are admirably stated by Prof. J. Perry, F.R.S., in his 
“ Applied Mechanics,” p. 80, 1909. See next page. 

As possibly some of the readers of this book may wish to 
make experiments on friction, I now describe a simple method 
whereby the relationship between the load moved along a 
plane and the force required to move it may be discovered. 


1834; Hirn : his results are collected in “ Introduction a la Mecanique Indus- 
trielle,” J. V. Poncelet, 3rd ed., Paris, 1870 ; Poncelet, “ Introduction a la Mecanique 
Industrielle,” Paris, 1870; Ball, “Experimental Mechanics,” 1871; Thurston, 
“ Friction and Lubrication,” New York, 1879 ; Galton, Engineering , Vol. XXV. ; 
Beauchamp Tower, Proc. Inst. Mech. Engs., 1883-5 ; Jenkin and Ewing, Phil. 
Trans., Vol. CLXVII., Part II.; Moseley, “ Mechanical Principles of Engineering ”; 
Reynolds, O., Collected Papers, pub. Cambridge University, and Ency. Brit., 
Vol. XXX., p. 372 ; Perry, J., “ Applied Mechanics,” Cassell, London, 1897. 

For friction in connection with belt gearing, see Trans. American Soc. Mech. 
Eng., Vol. VII., p. 347, containing researches of Prof. Lanza, also the same society, 
Vol. VII., p. 549 ; Lewis, Vol. XV., p. 204 ; F. W. Taylor should be consulted. 
See, too, the admirable treatment of the subject of belt and rope gear in “ Elements 
of Machine Design,” Part I., by W. C. Unwin, F.R.S. ; and Report and Observa¬ 
tions on the Lille Experiments upon . . . Ropes for the Transmission of Power, by 
Prof. Capper, 1895, Inst. Mech. Engs., London. 


FRICTION 


19 


Professor Perry’s Comparison between Solid and 
Fluid Friction. 


Friction between Solids. 


Fluid Friction. 


(1) The force of friction does not 
much depend on the velocity, 
but is certainly greatest at slow 
speeds. 


(1) The force of friction very 
much depends on the velocity, 
and is indefinitely small when 
the speed is very slow. 


(2) The force of friction is pro¬ 
portional to the total pressure 
between two surfaces. 


(2) The force of friction does not 
depend on the pressure. 


(3) The force of friction is inde¬ 
pendent of the areas of the 
rubbing surfaces. 

(4) The force of friction depends 
very much on the nature of the 
rubbing surfaces, their rough¬ 
ness, etc. 


(3) The force of friction is pro¬ 
portional to the wetted surface. 

(4) The force of friction at 
moderate speeds does not much 
depend on the nature of the 
wetted surfaces. 


Experience shows that almost any experiment carefully made 
to discover some physical condition is the most valuable way 
of acquiring knowledge about it. It is certainly far the most 
lasting in the memory. 

When two surfaces are in contact, such as a book resting on 
a table, it will be found that if the book is made to slide along 
the table a certain force, acting parallel to the surface of the 
table, must be applied to the book in order to maintain uniform 
motion. This resistance to motion which is experienced is 
due to the force of friction. In order to obtain a numerical 
value of this force some such apparatus as that which will now 
be described may be used. 

In the apparatus usually employed for showing the laws of 
friction the moving force is measured by some mechanism 
external to the body moved ; this introduces a small unknown 
amount of friction due to itself, but for this a correction can 
be made. A plank of deal or any other suitable wood, about 
5 feet X 9 X 2 inches, furnished with two ribs of wood fixed to 
its under side so as to support it from sagging, is carefully 
planed and surfaced. The sliding piece (which will be called 
the slide) is made of the same kind of wood 8x8x2 inches. 

c 2 






20 


DYNAMOMETERS 


A cord fixed to an end of the slide passes over a pulley ; 
to its end, which hangs down, a cylinder open at the top is 
suspended. Into this cylinder, which should be 12 inches long 
and 3 inches in diameter, dry sand is allowed to run in a fine 
stream ; when the weight of the cylinder and sand has imparted 
to the slide a steady, slow motion, the flow of sand is stopped 
and the cylinder and sand weighed. The weight of the cylinder 
should be found and marked on it so that only the sand has to 
be weighed in each of a set of experiments. In each experi¬ 
ment the weight of the slide W must be altered ; it is con¬ 
venient to make the minimum weight of the slide, say 4 pounds, 
and then to add 4 pounds for each new experiment. The moving 
weight F must also be found in pounds and decimals of a 
pound. It will be found that the ratio of F to W is approxi¬ 
mately a constant quantity. How, then, can we obtain a 

F 

trustworthy value for the quotient which equals the co¬ 
efficient of friction ? This is usually denoted by the symbol p. 

The answer to this question is : A large number of experi¬ 
ments must be made and tabulated, and the best value found 
by the method of least squares, or by a graphic method which 
will be described. 

In eight experiments the following numerical values were 
found :— 


Table I. 


No. of 
Experi¬ 
ment. 

R 

Total Load 
on Slide in 
pounds. 

Corrected 
Mean Value 
of Friction. 

F 

Calculated 
Value of 
Friction. 

Difference of 
Obs. and Cal. 
Values. 

1 

14 

4-7 

5-0 

+ 0-3 

2 

28 

8-2 

8*5 

+ 0-3 

3 

42 

12-2 

12-0 

- 0-2 

4 

56 

15-8 

15-6 

- 0-2 

5 

70 

19-4 

19-1 

- 0-3 

6 

84 

23-0 

22-6 

- 0-4 

7 

98 

25-8 

26-1 

+ 0-3 

8 

112 

29-3 

29-7 

- 0-4 









FRICTION 


21 


Method of Least Squares. 


[“ A number of observations being taken for the purpose 
of determining one or more unknown quantities, and these 
observations giving discordant results, it is an important 
problem to determine the most probable values of the unknown 
quantities. The method of least squares may be defined to be 
that method of treating this general problem which takes as 
its fundamental principle that the most probable values are those 
which make the sum of the squares of the residual errors a mini¬ 
mum." This is the opening paragraph in the chapter on The 
Method of Least Squares in “ Spherical and Practical 
Astronomy,” Vol. II., p. 469, by Chauvenet. It is a conse¬ 
quence of the theory of probability that if a very large number 
of observations are made with a view to find some unknown 
quantity a more probable value of this quantity is obtained if 
the sum of the squares of the errors in the several observed 
results is made a minimum than if merely the algebraic sum 
of the errors is made zero. The latter corresponds to the 
arithmetical mean of the observations. It should be remem¬ 
bered, however, that the method of least squares is only 
properly applied where the number of observations is very 
great. With a small number only the use of the method is 
undesirable, in fact, it is merely a waste of time.] 

If K is the coefficient of friction, we have to find the best 
value of K from sets of experiments made with different loads, 
which, when put into the equation F — KR = 0, will make 
F — KR as close in value to 0 as possible. If R l5 R 2 , R 3 , R m , 
etc., are the loads on the slide, and F„ F 2 , F 3 , F m the forces 
which act in each case, then we have to find a value of K, 
which makes 


u< 


= (F, - KR,) 2 + (F 2 - KR 2 ) 2 + (F 3 - KR 3 ) : 


+ (f,-kr m y 

a minimum. Let u 2 equal this sum. 
u du = 0 = - R 1 (F, - K,R,) dK, - R 2 (F 2 - K 2 R 2 ) 
... — R m (F w — R W R W ) c£K to 
equating to zero the coefficients of cZK„ dK 2 . . . 

xf _F 1 R 1 „ _f 2 r 2 f-R. 

. . JV, p 2 5 IXo r. ... -IV,, 


dK,, 


Ri 2 

(K 1 R 1 2 + K 2 R 2 2 + 
taking K as the mean value, K 


R 2 2 


2F,R, 

iR, 2 ' 


R» 

K,„R,„ 2 ) = SFiRi. 






22 


DYNAMOMETERS 


For convenience of calculation let the loads R 1; R 2 , R 3 , • • • 
R„„ have the values W, 2W, 3W, . . . mW, 
so that SF,R, = WF, + 2WF2 + 3WF 3 + . . . + MWF» 
= W (F x + 2F 2 + 3F S + . . . + MF m 
and SR^ = W 2 + (2W) 2 + (3W) 2 . . . + (MW) 2 

= W 2 (l + 2 2 + 3 2 + . . . +m 2 ) 
m (m + 1) (2m + 1) 

6 

Y _ n F +2F 2 + 3F 3 + . . . + ^F m 

' ‘ W m (m + 1) (2m + 1) 

Taking the values from the table,* 

m = 8, W = 14. F x + 2F 2 + 3F 3 + m¥ m = 770 9. 

. K = 0 27. 

It has been found that an equation of the form F = x + 2/R 
exhibits the results of values found by experiment more 
accurately than the former equation, F = &R. It may be 
established thus. 

We cannot find values of x and y, such that the equation 
will be satisfied for all values of F and R, taken in pairs. But 
by the doctrine of least squares we know that the best values 
of x and y will cause the value of 

(Fi — x — yRi) 2 + (F 2 — x—yH 2 ) 2 + . . . + (F w — x — yRj 2 
to be a minimum ; let it = u 2 . This expression must be 
differentiated with respect to x and also y and the differential 
coefficients equated to zero. 

m 2 — (Fi/Ri) 2 -f (F 2 — x + yR 2 ) 2 + . . . + (F w — x — yR Hl ) 2 
udu — 2 (F 1 — x — 2 /R a ) (— dx — R x dy) 

+ . 

+ 2 (F m — x - yRJ {—dx — R m dy) 
equate to zero coefficients of dx and of dy. 

. •. 2(F — x — yR) = 0 and 2R (F — x — yR) = 0. 

Take R x = W, R 2 = 2W . . . R /)? = mW, 

then F t — x — yW = 0 

F 2 — x — y 2W = 0 


F m — x — ymW = 0 

Fi + F 2 + . . . + F w — m x — yW (1 +2 + 3 . . . + m) = 0 
CallF 1 d-F 2 d- . . . F m = A, 

then A - mx - 11 ?/ W = 0. . . ( 1 ) 


* This was constructed from the data of eight experiments, Table I. 







FRICTION 


23 


also WF, — xW — yW* = 0 

2WF 2 — 2xW — y{ 2W) 2 = 0 

MWF„ - mxW —- y(mW) 2 = 0 
Call F, + 2F 2 + . . . MFto = B, 

then W R -m ™ (w + *1 < 2w + W*y _ 0 

(2w + l) Wy = Q _ (2) 

From equations (1) and (2) we find 

x = Z±*m A _^_ B 

m 2 —m m 2 —m 
_ 12 B 6 A 

^ m 3 — m W m 2 — m W' 

In making the experiment care should be taken to make the 
load on the surface of the slide equal to W, 2W, 3W, and so 
on. This simplifies the calculation, and enables us to sum the 
numbers 1 + 2 + 3 + m and also the squares of these numbers 
by means of known formulae. 

The method of finding x and y in the equation 
F — x — yR = 0 

has now been demonstrated, so that with this equation we 
have friction = a constant + coefficient of friction X load. 
By taking values of R and F from Table I. the equation 
becomes 

F = 1-44 + 0-252 R, 

but it must only be applied to weights which lie within the 
limits of the values found by the experiments and shown in 
Table I. 

I am indebted to Sir R. Ball, F.R.S., for the table taken 
from his excellent book on “ Experimental Mechanics ” 
(Macmillan) and the matter respecting the method of least 
squares, which has been slightly altered in order to show each 
step in the formation of the equations. 

Diagram on Squared Paper. 

If we wish to exhibit the values given in Table I. graphically 
we proceed thus (squared paper divided in tenths of inches will 
be found suitable for the purpose). Along the line OR, Fig. (3). 
we set off the values of the loads R on the slide and their 











24 


DYNAMOMETERS 


corresponding ordinates, showing the values of F for each value 
of R. The points on the squared paper at the top of each 
ordinate should be marked with a dot surrounded by a very 


small circle. The circle makes 



the next operation easier to 
perform. A fine black 
thread is stretched 
from the extremities of 
a small bow of wood 
or whalebone and 
placed so as to take 
a mean position 
amongst the dots ; the 
point at which the 
thread cuts OF is 
marked ; its distance 
from 0 shows the value 
of the constant in the 
•equation, and the tan¬ 
gent of the inclination 
of the thread to OR 
gives very approxi- 
co mately the value of 
^ 6 the coefficient of R ; 
o ^ so that by means of 
« a carefully constructed 
diagram we can exhibit 
the relationship of R 
and F, and it becomes 
a descriptive picture 
* of the equation con- 
£ necting the variable 
*§ quantities found by 
3 experiment. For in¬ 
stance, the equation 
F = 1*4 + 0252R is 
represented by the 
straight line of the 
diagram, if we take 
R = 70, F == 19-0 
from the equation. 






















































































FRICTION 


25 


And taking 70 on the line of loads on the diagram we find 
F = 19 + some very small quantity. 

Almost innumerable examination papers on mechanics have 
been set and answered without any allusion whatever being 
made to friction ; and the impression left on the mind is that 
the papers must have been the product of those who must 
regard friction in mechanics as of but little importance. 
Probably friction has been omitted because it would introduce 
a little more difficulty into the solution. But the practice of 
neglecting it is simply vicious, since in every real, material 
mechanical contrivance friction exists, either for good or evil, 
and should be thoroughly appreciated by the student of 
mechanics and the engineer. “ Friction is, so far as we are 
concerned, quite as essential a law of Nature as the law of 
gravity,” writes Sir R. Ball. 

Many of the examination papers, if somewhat remodelled, 
become interesting—that is, after friction has been correctly 
introduced—and the weightless cord has been replaced by 
something which really exists. A single question containing, 
as far as is known, the real conditions of the case is better 
worth answering than a thousand in which the many insepar¬ 
able conditions are neglected. 

[Where the number of observations is so small as eight, as 
in the instance last considered, even where the form of the 
equation connecting the observation and the calculated result is 
accepted—in this instance F = &R or F = x + yR, as the 
case may be—the graphical method gives all the information 
which can properly be derived from the experiments, provided 
only that the scale is such that the uncertainties of observation 
when making the experiment are considerably greater than 
the uncertainty in the comparison on the diagram of the 
position of the points representing individual observations 
and those where the line representing the accepted law cuts 
the corresponding ordinates. Any apparent increased accuracy 
resulting from pushing the method of least squares to an 
extreme is entirely fallacious. If, as in the example here given, 
the observations are not numerous and the conditions are con¬ 
stantly changed so as to cover a large range in the values of 
the abscissae, the graphical method is greatly to be preferred 
to any treatment of the figures by the method of least squares 


26 


DYNAMOMETERS 


in relation to a particular law, for, if, as in this instance, the 
law is empirical and not a law of Nature in itself absolutely 
true, the distribution of the points representing observations 
with respect to the line representing the empirical law them¬ 
selves throw some light upon the propriety of accepting the 
law. We have already seen that the simple and imaginary law 
of friction F = &R does not agree with experiment so well 
as the less simple law F = x + yR, but it cannot be inferred 
from this that this more accurate law is itself a true law. 
The diagram (Fig. 3) at once shows that the second law is a 
better representation of the fact than the first, but the “ errors,” 
that is, the distance of the points within circles from the 
straight line, have a certain consistent character. For abscissae 
below 35 and above 90 they are below the straight line, while 
between these values they are above. With so small a number 
of observations it is not possible to assert that these divergencies 
indicate a truer law than that represented by the straight line. 
If, however, a repetition of the experiments consistently 
showed corresponding “ errors,” then the conclusion would be 
that a more complex law would be needed to represent the 
truth. Thus, if the graphical method is used on a scale large 
enough as already defined, not only may the constants relating 
to an assumed law be determined, but the propriety of the law 
may be ascertained, both in a minimum of time. 

Where the law to be represented on squared paper is not of 
the form y = a bx it cannot be directly represented by a 
straight line. By the use of specially-ruled paper other laws 
may be represented by lines either straight or more simple in 
character than those which would be required upon paper 
ruled in equal squares. The most useful special ruling next to 
that of equal squares is the logarithmic ruling ; that is, the 
distances on the paper are proportional to the logarithms 
of the numbers attached to the corresponding lines. Such 
paper may be bought already ruled or it may be extem¬ 
porised by copying the distances from an ordinary slide 
rule and marking the main lines 1, 2, 3, etc., up to 10, after 
which it is unnecessary to repeat the ruling. On this 
paper (see Fig. 57, page 118) the law y = ax 11 can be repre¬ 
sented by a straight line making an angle of tan — l n with 
the axis of x. If n is negative as in the case of Boyle’s law, the 


FRICTION 


27 


straight line slopes downwards instead of upwards—at an angle 
of 45 degrees in this case. All such lines represent x 11 , and the 
particular line is determined by the constant a. Another 
system of ruling (Fig. 4) with one set of lines spaced equally 
and the other logarithmically enables one to represent com¬ 
pound interest growth or logarithmic relations as a straight 



Fig. 4. 

line. In Fig. 4 only one line in every 10 of the slide rule is 
drawn, to avoid confusion on the reduced scale. On ruling 
any straight line on such paper the value of the series of points 
on the equally-spaced lines are in arithmetical progression, 
while those on the logarithmically-spaced lines are in 
geometrical progression. Any straight line ruled through the 
point 0 on the equally-spaced set and 1 on the logarithmically- 


































































28 


DYNAMOMETERS 


spaced set provides a table of logarit ms to some base. If it 
also pass through the corresponding point 1, 10 on the two 
scales the table of logarithms is to the base 10, for the logarithm 
of 10 to the base 10 is 1. Also the logarithm of e, the value 
of which is 2-7183, to the base 10 — -43429 the modulus. If 
the tangent of the inclination is increased in the ratio of 
1 : 2-3026, so that the line passes through the point 2-3026, 
10, then the table of logarithms is to the base e, for log e 10 is 
2-3026. Also the logarithm of e to the base e = 1. Log 
1=0 according to any system, so all these lines must pass 
through the point 0, 1. 

If in experiments on the friction of ropes or belts round 
drums, referred to in the next few sections, the angles, however 
measured, are plotted on the scale of equal parts and the 
observed pairs of tensions on the logarithmic scale, the line 
joining the corresponding points should be a straight line 
according to the theory as there expounded, and the agree¬ 
ment or otherwise of a number of experiments with one another 
can be ascertained immediately by inspection with an accuracy 
greater than that of the experiments. In plotting the pairs of 

T 

tensions the smaller should be plotted as 1, and the ratio 

2 

should be plotted as the other. The straight line passing 
through the point 0, 1, and as evenly as possible through the 
plotted points, represents the growth of the tension in the 
band. The quantity /jl9 may be read directly from the line 
giving logarithms to the base e, for this line cuts the line 
T 

representing on the logarithmic scale at the point where the 

4 2 

scale of equal parts shows the value of [x9 , and thus /x may be 
determined, but for this 6 must be taken in radians, not in 
degrees, half-turns, or other arbitrary measure.] 

The value of the friction of a band on a cylinder at any 
point in the arc of contact may be shown graphically by Prof. 
J. H. Cotterill’s method as follows. 

Let PQ (Fig. 5) be a section through the cylinder perpen¬ 
dicular to its axis, and let AB be an element of the band which 
embraces it, also let T 1} T 2 be the tensions on each side of the 
element, let the value of T x — T 2 be such that the belt is on 
the point of slipping. Then AB is kept at rest by T x and T 2 


FRICTION 


29 


and the reaction against the cylinder R. The three forces 
meet at the point D. On OA set oil 0 a to represent on any 
convenient scale the value of T 1? draw ab perpendicular to R 
cutting OB in b ; then, since the sides of the triangle abO are 
perpendicular to T 1? T 2 , R, they are proportional to T l5 T 2 , R, 
and Ob represents T 2 and ab, R. If AB be made very small, 
i/j will be the angle of friction. Commencing the construction 
at M and continuing it to N, a curve is described the radius 



vector of which shows the value of the tension at any point. 
Also from a consideration of the diagram a useful formula may 
be constructed, thus : 

Draw C a, E5, at right angles to OB and OA respectively, then 

aC 

T 7 0 a sin 0 ba _ ab _ cos Cab _ cos (9 — F) 

% = Ob ~ sin 0 ab ~ 5E “ cos E ba ~ cos * 
ab 

= cos 9 + sin 9 tan F. 

If 9 diminish indefinitely, cos 9 becomes = 1, sin 9 = 9 

and ^ = 1 + 9 tan F, or —" — ? ^ an 

1 2 -*-2 












30 


DYNAMOMETERS 


Let T x — T 2 = dT in the limit, and <p = d9, 

then tan L = ^ the coefficient of friction. 

1 do 

T p 

This on integration gives ^ = e^, 

where T p and T (/ are the tensions at P and Q respectively and 
6 is the angle in radians between OP and OQ. For a circular 
pulley the curve MaN is an equiangular spiral. 

Mechanical Method of Drawing the Logarithmic or 
Equiangular Spiral (by the author). 

The equation to the curve is r — a 0 , 

where r is the radius vector, 

a is a constant on which the form of the curve depends, 
6 is an angle swept out by the radius vector, 

X is an angle which the tangent to the curve at any 
point makes with the radius vector ; it equals 

tan- 1 —-—. 
log, a 

In the logarithmic spiral the angle at the pole increases in 
an arithmetic ratio, while the radius vector increases in a 
geometric ratio ; so that the angle generated by the radius 
vector is proportional to the logarithm of the length of the 
radius vector. The spiral is called equiangular, because the 
tangent at any point in it makes a constant angle with the 
radius vector. I have taken advantage of this property of the 
curve, and embodied it in the instrument now to be described. 

A surface such as a drawing-board is covered with paper 
which receives the trace made by a small sharp-edged wheel. 
This wheel rotates in a forked bearing, its axis being parallel 
to the plane of the paper. The plane of rotation of the wheel 
may be placed at an angle to the longitudinal axis of the radius 
bar. This radius bar is free to slide through a vertical axis, 
taking the form of a small pillar erected on the board. When 
the radius bar rotates about the pillar and the plane of the 
wheel is at right angles to it, the path of the wheel is a circle, 
but if the plane of the wheel be set at some angle X less than 
90 degrees to the radius bar, it will traverse over the equi¬ 
angular spiral, for it moves continuously tangential to its path. 



FRICTION 


31 


Clear traces may easily be obtained by placing carbon paper 
over the paper on which the trace is required and weighting 
the wheel enough to make it mark the paper under it as it 
rolls. 

Instruments of the kind described, made from my designs, 
have been used by me in the Engineering Laboratory, Oxford, 
for showing the growth of the curve r = a 6 , and one was 
added in the year 1886 to the collection of apparatus in the 
Physical Laboratory of Winchester College so admirably 
organised by Mr. W. B. Croft. 

In order that the instrument may be applied to an experi¬ 
ment on the friction of a belt on a pulley, the wheel (called 
the tangent wheel) must be set at the angle x to the radius 
vector. To do this we must know the values of T 2 and T x 
and the angle 6 between the two radii vectores r 2 , r v which 
are proportional to T 2 and T v Let the angle 6 be measured in 
radians. 


Then tan x 


6 log 10 e 


logufa - lo gio^i 
For example, suppose the belt to make half a turn on the 
pulley and the tension of one end to be double that of the 
other, or in symbols— 

let (9 = tt = 3*1416 


let - 2 = 2 

r i 

log 10 e = 0*43429 

then tan x = 4*5324 and x = 77° 33' 29", 
and since r = a and tan x 


log] 


log, 


•43429 


= -095818, 


tan x 4*5324 
whence a = 1*2469 and the equation becomes 
r— 1*2469®; 

when 6 = o, r = 1, when 6 = it, r = l*2469 7r = 2. 

[The tangent wheel is to be set so as to make an angle of 
77 ° 33 ' 29" with the radius vector, or as near that as possible, 
and the instrument made to trace the curve for an indefinite 
number of turns. It will then be found that if any straight 
line be drawn through the pole, at which point the pillar is 
fixed, it will cut the spiral in a number of points, and that the 
ratio of the distances from the pole of any two such consecutive 







32 


DYNAMOMETERS 


points on the curve is as 2 to 1 , agreeing with the assumed 
condition that the belt should double in tension in one half- 
turn. 


T r 1 

Since ~ = — = e* 6 — 2 

12 ^*2 

flO = fJLTT = log*2 

fjLTr = *69314 

/j, = * 221 . 

So -221 is the coefficient of friction under which a belt doubles 
in tension for every half-turn that it makes. 

The evaluation of /x when e^ 9 is known is tiresome rather than 
difficult. This can be effected with abundant accuracy by 
means either of the semilogarithmic chart (Fig. 4), already 
described, or of the slide rule with a log log line, invented early 
last century by Dr. Roget and reinvented several times since, or 
the exponential curve of Fig. 7 may be used. Calling the log log 
line of the rule the P line and one of the ordinary log lines the 
C line, it is merely necessary to set log e 10 or 2-3026 on the 


T r 

C line opposite 10 on the P line, then opposite ~ or — or the 

- 1-2 ^*2 

ratio of the tensions of the ends of the belt on the P line will be 
found y9 on the C line. This product can be divided by 0, or 
in the last instance by 7 r, on the A and B lines or upon another 
rule, and thus /z may be found very quickly. Where a large 
number of experiments have to be reduced this is preferable 
to the usual treatment with logarithm tables, as the whole 
series of values of /x 0 can be read from a single setting of the 
rule, and the accuracy is sufficient. The semilogarithmic 
chart is almost equally convenient.] 


Automatic Friction Machine. 

The Relationship between the Diameter of a Pulley and the 
Coefficient of Friction of a Band in Contact with the Pulley. 

It has been shown by the experiments of Imray that with 
pulleys widely differing in diameter the coefficient of friction 
is nearly the same. 

His experiments were made thus : a pulley was held fast 
on a horizontal axle, a belt embraced half its circumference, 
and weights P W were suspended from its extremities. The 


FRICTION 


33 


weight W was gradually increased, until the belt just began 
to slip ; the value of (W — P) equalled the frictional resist¬ 
ance between the pulley and the belt. From data so obtained 
W 

the ratio — was determined : if then when the arc of contact 

W 

embraced by the belt is constant the ratio -p remains invariable, 


F 



Fig. 6. 

when the diameter of the pulley is changed, then the resistance 
of friction does not depend on the diameter of the pulley. 

When making experiments myself on this subject consider¬ 
able difficulty was experienced in determining the exact 
weight which caused the belt to slip ; after several attempts, 
the following plan was devised by me, whereby the value of W 
at the instant of slipping was automatically recorded. Tho 
arrangement of the apparatus is shown in the diagram (Fig. 6), 
in which A is the fixed pulley and B D the two weights sus¬ 
pended from its ends. The weight D is furnished with a 
^ D 














34 


DYNAMOMETERS 


hollow cylindrical vessel C of known weight w ; the vessel is 
filled with water from the tube NM ; the water can be instantly 
stopped by the edge of a metal plate M when released by an 
electromagnet K on to a piece of rubber tube L. 

The instant the belt begins to slip the projection E touches 
the electrical contact piece F ; it is released from the contact G 
and the current from the battery H is broken ; the supply of 
water through MN ceases, so that if the water in the vessel 
be drawn off at Q and weighed the exact difference of the pulls 
on the two sides of the belt may be ascertained. 

To return to Imray’s experiments : five pulleys were used 
of small diameter, ranging from 5*5 inches to 14 inches ; the 
rounding of the face of the pulley was about Q-125 inch in 
2 inches ; the surface was polished, and the same belt was 
used in each experiment, being oily and pliant; its width 
was T62 inches and its thickness 0T2 inch. The results 
obtained are embodied in the following table :— 

Table II. 


No. of 

Diameter of 

Weight of 

Weight of 

Value of 

Mean Value of 

W 

Experiment. 

Pulley, inches. 

P, in lbs. 

W, in lbs. 


P • 

1 

) ( 

18 

29 

1-611 

J 1-675 

2 

5-5 

34 

57 

1-676 

3 

) ( 

65 

113 

1-738 

) 

4 

1 7-6 ! 

17 

29 

1-706 


5 

32 

57 

1-781 

j 1-733 

6 

) i 

66 

113 

1-712 

7 


17 

29 

1-706 


8 

i » j 

32 

57 

1-781 

1-733 

9 

66 

113 

1-712 

) 

10 

j 1.8 j 

18 

29 

1-611 

) 

11 

34 

57 

1-676 

1-642 

12 

69 

113 

1-638 

) 

13 

( 14-0 j 

17 

29 

1-706 

) 

14 

34 

57 

1-676 

1-673 

15 

J l 

69 

113 

1-638 

) 


Average value of -p = 1-691. 


The experiments show that the friction in the case of the 
largest pulley was almost the same as that of the smallest 










FRICTION 


35 


one ; from the agreement of these fifteen experiments it may 
be inferred that the amount of friction is not affected by the 
diameter. 

In the formula for the friction of a belt on a pulley, namely, 
l°»e p" = ^0, in which W and P are the two loads, p, the 

coefficient of friction, and 9 the angle in radians embraced by 
the belt, and e = 2-71828.., the diameter of the pulley is 
not involved. When a driving-belt slips on a pulley owing 
to overload, the slip may be prevented by employing a pulley 
of greater diameter ; this does not increase the friction, but 
since the circumferential velocity of the larger pulley is greater 



than the smaller one, the friction necessary to transmit the 
same power at the same number of revolutions per minute is 
proportionately less, and so may be reduced below the slipping 
limit.* 

* [Note. —There is a useful limit to the size of a pulley in any case, determined 
by the centrifugal force of the belt itself, which diminishes the pressure of contact 
between the belt and the pulley and hence the friction. For a belt of any material 
there is a practical working limit to its longitudinal tension. If M is the number 
of pounds per foot run (mass per unit length) and V the linear velocity of the belt 
in feet per second, the longitudinal tension needed to balance the centrifugal force 

may be shown to be pounds, and this is independent of the diameter of the 

pulley over which the belt runs. With such a tension only in the belt there is nothing 
available for friction, so the tension necessary for tne frictional drive must be 
additional and it is only this add tional tension which is effective. With increase 
of diameter of pulley the work due to a given effective tension increases in direct 
proportion, while the tension needed to balance centrifugal force increases in 
squared proportion. So when this is subtracted from the safe tsnsion of the belt 
the work which can be transmitted, far from increasing indefinitely with the 
linear speed, is a maximum at some speed which depends on the ratio of the safe 

D 2 


































36 


DYNAMOMETERS 


This equation is exhibited diagrammatically in the curve 
W 

Fig. 7 , and the ratio p can be found at once for different values 

of /x and 6. Suppose /x = 0-33 and 6 = 2, then fid = 0-67 ; 
read this value along the base line, the corresponding ordinate 
W 

= 1 * 95 , the value of p. The curve is drawn thus : the base 

line is divided into tenths of some unit up to the value 2 . 
The product ji6 is given values from 0 to 2 . The curve drawn 
through the corresponding ordinates is the required one. The 
results of experiments on larger pulleys are exhibited in the 
following table :— 


Table III. 

Friction of Belts on Pulleys of large Diameter, with 
variable Arc of Contact. 


No. of 

Diameter 

Arc of 

Value of 

Value of 

Ratio of 

Mean 
value of 

Calculated 
Value of 

Error 
per cent. 

Experi¬ 

ment. 

of Pulley. 
Inches. 

Contact. 

Degrees. 

P 

in lbs. 

W 

in lbs. 

W 

P‘ 

W 

P* 

W 

P’ 

29 

) 

( 

14 

25 

1*786 

) 



30 

15-8 

120 

42 

84 

2-000 

1*962 

1*938 

11 

31 

) 

( 

70 

147 

2*100 

) 


32 

) 

( 

14 

24 

1*714 

\ 

1 



33 

24-0 

123 

42 

78 

1*857 

1 

1*809 

1*778 

if 

34 

) 

l 

70 

130 

1*857 

1 

1 



35 

] 




14 

34 

2*429 

] 

1 




36 





16 

39 

2*437 




37 

38 


i 38*8 

144 < 

| 

i 

21 

28 

52 

70 

2*476 

2*500 


> 2*506 

2*491 

l 

39 





42 

109 

2*595 





40 


1 


l 

70 

182 

2*600 

J 





The 


calculated value of 


W 

P 


was obtained by taking 


fi — 0*316, as deduced from the experiments tabulated in 


working tension to the weight of the belt per foot. Thus leather belts should not 
run more than about 4,000 ft. per minute, hemp or cotton ropes about 6,000, while 
steel bands or ropes may run much faster.] 
















FRICTION 


37 


Table II., and reducing the arc in degrees of Table III. to 
circular measure 9, and putting these values into 

W 

log. p- = 

The largest pulley appears to have given the greatest 
friction, but the experiments on the smallest pulley show more 
friction than those on the pulley of intermediate size. Such 
a discrepancy has been accounted for by the difference of 
polish of the surfaces. The result with any one of the pulleys 
does not vary from the average more than by a small quantity, 
which might be accounted for by the difference of polish 
mentioned. This appears to have been the opinion of Imray. 
In all belt friction experiments it is no easy matter to deter¬ 
mine the exact amount of arc of the pulley in contact with 
the belt. Fig. 8 shows how the length of arc RS is regulated, 
by means of a small pulley on the right, carried on an arm 
free to rotate about C. The small pulley must not touch the 
large pulley, though it is made to do so in the figure. 


Table IV. 

Experiments with the Automatic Friction Machine (by 
the author). A cotton rope (lj inch circumference) was 
used on a V-grooved pulley, well polished but not 
lubricated. 


No. of 
Experi¬ 
ment. 

Weight 

P. 

Weight 

W. 

Ratio 

W 

P- 

Mean 

W 

P* 

Log W 

10 P- 

Diameter of 
Pulley 
V-grooved, 
in feet. 

fl 

145-8 

336 

2-304 


•3625 

1 

2 

75-5 

220 

2-925 

1 

•4661 

1 

A 3 

110 

295 

2-681 

!• 2-806 

•4283 

1 

i 4 

75-2 

212 

2-819 

•4501 

1 

15 

40 

112 

2-800 

J 

•4472 

1 

fl 

181-5 

445 

2-451 


•3893 

0-5 

1 2 

40 

122 

3-050 

1 

•4843 

0-5 

B i 3 

75 

228 

3-040 

! O.QO A 

•4829 

0-5 

i 4 

145-5 

369 

2-536 


•4041 

0-5 

15 

110-5 

295 

2-669 

J 

•4264 

0-5 















38 


DYNAMOMETERS 


In experiments 1 A and 1 B. The result is affected by too 
great a load, and the rope was deformed in section. Experi¬ 
ments 2—5 A and 2 —5 B give better results, and these only 
are taken to find the mean values. 

The quantities W, P, /a and 0 are connected together by the 
equation 



the generation of which has been already shown. In these 
experiments the rope embraced half the pulley so that 
0 = 77 . e = the base of the hyperbolic logarithms, and 



and, finding the value of /a from this equation and using the 
mean values in set A and set B, we find 


for set A, /a = 0*328, 
for set B, /a = 0*330. 

Since in the experiment described the rope rested in a 
V-groove, if the radial force Q be taken as unity the whole 
normal pressure R between the sides of the V-groove and the 
rope is Q cosec 9 , where 29 = the angle of the groove, so that 
R = Q cosec 9 . And the resistance to slipping is 
/aR = pQ cosec 9 . 


If /jlO cosec 9 be written for fiO in the equation ^ — ef 10 , we 

rji J-l 

have an equation, ~ =*= epO cosec 9 , which is applicable to the case 

-*-1 

of a rope lying in a V-groove. 

[An instructive experiment on the same subject requiring 
the minimum of apparatus may be made by means of an 
umbrella, a spring balance, and a piece of tape. Hang the 
balance from a bracket and fasten one end of the tape to the 
balance ; pass it under the hooked handle of an umbrella and 
hold the free end in the hand so that both ends of tape are 
vertical. When raising the hand, the umbrella will appear to 
weigh less than it does when the motion is in the opposite 
direction. The sum of the two readings on the balance M 
will be found to be equal to the weight of the umbrella when 
suspended directly. The two readings give T x and T 2 , and 
quite good observations may be made in this way. 


FRICTION 


39 


The extremely rapid increase in the friction between a rope 
and anything round which it is wound as the angle of winding 
is increased is referred to in a subsequent chapter, more 
especially in relation to bollards and capstans. This principle 
is also made use of in drawing wire. It would be impossible 
to draw wire through a number of draw-plates in series by 
pulling at the end, for each draw-plate requires a force com¬ 
parable with the breaking load of the thinner wire leaving it 
to draw the thicker wire through. As the wire leaving each 
plate runs at a higher speed than it did in entering the plate it 
would be impossible to give suitable movements to the parts 
between successive plates by any direct gripping device, for 
if the pull on any one of the finer parts of the wire leaving a 
plate were ever so little too rapid to correspond with the 
slower motion of the thicker parts entering the plate the wire 
would break instantly, whereas if it were too slow the wire 
would accumulate between the plates and become entangled. 
The whole difficulty is overcome by placing between each pair 
of plates a smooth revolving wheel round which the wire 
makes a turn. Only beyond the last plate is the wire wound 
up positively on a moving drum. All the intermediate wheels 
are made to turn at speeds somewhat in excess of those neces¬ 
sary at the corresponding points, but they only draw the wire 
through the preceding plate at the exact speed required to 
feed succeeding plates, for it is only at this rate that there is 
any tension on the wire leaving the wheel, and this is 
magnified in the ratio of 1 to e 2,lir for the one turn round the 
wheel. 

A capstan or one of the wheels between a pair of draw-plates 
just described is really a mechanical relay. A smaller force 
applied to the end of the wire or cable leaving the capstan or 
wheel is magnified in a definite ratio, which ratio may be made 
small or very great as required by making the angle of wind 
moderate or great, as already sufficiently explained. It is a 
mechanical relay in two senses ; either a force magnified in 
the desired ratio may be applied to a support yielding, for 
instance, under an elastic law, when the displacement of the 
attachment from its zero position will at all times be propor¬ 
tional to the applied force, or again, if the magnifying power 
is sufficient to overcome the greatest resistance to be met; 


40 


DYNAMOMETERS 


with, the relay is of a different type, copying the movement 
but disregarding the opposition. 

Mr. S. G. Brown* has made use of this principle in one of his 
submarine cable relays, where the signalling current received 
by the wires a a is insufficient in strength to cause the receiving 
coil A to move the relay contacts. The receiving coil (Fig. 9) 
is suspended by a fibre in a magnetic field N S, and is so sup¬ 
ported that it can rotate through a small angle about a vertical 
axis. Two fibres s attached to the sides of the coil each take 
one or more turns round a drum D and then pass on to the arm 
of the relay R, to which they are fastened. The drum is kept 
turning towards the receiving coil, as shown by the arrow. 



When a signal current is received the tension in one or other 
of the fibres s is greatly magnified in the relay end of the same 
fibre t, so the relay faithfully follows the movement of the 
coil A even though the forces are magnified more than three 
hundred times. Thus the wire w is made -f or — in obedience 
to the signalling currents received by the coil A. 

Dr. J. G. Gray has made use of this form of mechanical 
relay in the gyrostatically controlled air- and water-ships which 
were described by him at a meeting of the Physical Society of 
London held on May 8th, 1914.f 

A similar arrangement with a known ratio of magnification 
would make the dynamometry of the work done in the most 
delicate instruments comparatively easy, or a succession of 

* Proceedings of the Physical Society, 1913, p. 131. 

t Proceedings of the Physical Society of London, Vol. XXVI Part IV 
June 15th, 1914. '* 














FRICTION 


41 


such relays, each of a size and strength suited to the forces met 
with, would steer a ship if desired with no greater controlling 
force than that due to a signalling current. 

In the author’s manuscript I found the following memo¬ 
randum, “Add note on Lateral Friction,” but he does not appear 
to have left any such note. This curious branch of the general 
subject is one which interested him greatly. Lateral friction is 
best defined by reference to an experiment which the author 
showed to me, which exhibits the phenomenon in a striking 
manner. On a horizontal shaft which can be made to turn at 
any desired speed fix a smooth cylindrical pulley and pass 
over this pulley a pliable belt, with a weight at one free end 
and with the other end fastened to the floor, so that when the 
pulley is turned in either direction the belt will slip upon it. 
The pulley should be several diameters above the floor. When 
the pulley is revolving and the band is at rest it will be found 
that the slightest lateral force applied to the belt will cause it to 
shift its position on the pulley. If the pulley is turning suffi¬ 
ciently fast the response is instantaneous, and the lateral move¬ 
ment is limited only by the attachment of one end to the floor. 
Forces far below that necessary to overcome the friction of 
the belt on a stationary pulley are immediately evident. 

The nature of lateral friction, or rather the reason for its 
absence, will be made clear by the consideration of an imaginary 
experiment with a block and an inclined plane. When the 
plane is inclined at an angle a below that which will cause the 
block to slide, the block may be pulled sideways by means of a 
thread, and then when the component of this lateral pull and 
W sin a due to gravity itself exceeds pW cos a, the block will 
move in the direction of this component force. Next suppose 
the block to be sliding down the incline very quickly and then a 
small lateral force to be applied by the thread, the block will 
then, as before, move in the direction of the component of the 
resolved force down the plane due to gravity and that applied 
by the thread, and this will be very slightly inclined to the 
direction of the greatest slope. Therefore, in proportion as the 
block is sliding the more quickly so will the lateral movement 
be the more rapid. As this experiment would be inconvenient 
to make, consider its equivalent when the block is supposed to 
be supported by and within a large hollow cylinder revolving 


42 


DYNAMOMETERS 


about a horizontal axis at a high speed. The block will take $ 
position within the drum having an inclination a, such that W 
sin a is equal to the running friction. Then a slight lateral 
force will have the effect of producing an immediate and rapid 
lateral response, and the fact that the relative path of the block 
on the surface is only slightly inclined to its former path will 
not be evident. The lateral motion alone is visible. Thus the 
more rapid the motion of the surface the more rapid the lateral 
response. There is the further peculiarity that the lateral 
friction is non-existent, for however small the lateral force may 
be the component of this and that due to friction parallel to 
the surface will have some inclination, and so the block will 
move sideways at a speed which is the same fraction of the 
speed at which the surface is moving as that which the lateral 
force is to the frictional force. 

This absence of lateral friction has been made use of in one 
of the forms of cable relay invented by Mr. S. G. Brown, in 
which a light pointer attached to a pivoted coil, through which 
the minute current from the ocean telegraph cable passes, 
rests very lightly on the surface of a polished silver drum kept 
in rapid rotation. The friction of the pointer, however lightly 
resting against a stationary drum, is vastly greater than the 
force available to move it, which is caused by the reaction 
between the minute current in the coil and the strong mag¬ 
netic field in which it is placed, and so if the drum were at rest 
no message would be received. As, however, the drum is kept 
revolving at a high speed, the pointer moves laterally under 
the feeble stimulus of the cable currents and the response is 
instantaneous. We are not concerned here with the electrical 
actions set up in consequence of this movement or with the 
other features of this ingenious instrument. It supplies, how¬ 
ever, an excellent illustration of the non-existence of lateral 
friction and of the instantaneous response to lateral forces, 
far too small to overcome the real friction. 

There is no difference in the action just described and that 
on a stationary belt of a pulley revolving within it. This 
action, however, differs entirely from the case of a running 
belt moved by a lateral force, as by a belt-shifter. All that 
happens when a lateral force is applied to the belt approaching 
a pulley is a slight angular deviation in the direction of the 


FRICTION 


43 


leading-in side, which does not slip on the pulley, but proceeds 
to trace out a helical path having the same angle. Thus if the 
belt is running fast a belt-shifter works easily and very quickly. 
It is useless to apply a belt-shifter to the belt where it leaves a 
pulley, but with a stationary belt over a slipping pulley it is 
indifferent whether the lateral force is applied on one side of 
the shaft or on the other. The contrast between a running 
and a slipping belt on the usual slightly convex pulley of a 
machine is even more striking. The running belt, if it is not 
central, acquires a lateral inclination always in such a direction 
as to make it ride up the conical side of the pulley on whichever 
side it may be, so any tendency to come off is always being 
corrected, and it rides quietly on the centre of the pulley. 
With a slipping belt, however, i.e., if it is not running sufficiently 
fast to counteract the effect of the slipping, the belt moves 
automatically towards the smaller portion of the cone, and so 
rides off indifferently on either side, according to the direction 
in which it happens to start.] 


CHAPTER III 


PLANIMETERS, ETC. 

PAGE 

The earliest application of the area method for finding the product of force 

and space : the Watt-Southern steam engine indicator ... 44 

Recording apparatus used in conjunction with work-measuring machines . 45 

General Morin and Ernst integrator ..... 

Disc and roller ......... 

Ashton and Storey steam engine integrator .... 

Record of work on paper band ...... 

Application of method by Mr. A. Denny, and by Herr Frahm . 

Two integrators by the author ...... 

The area of a figure, how found ...... 

References to authors of papers on integrators and planimeters . 

Description of the Amsler planimeter, showing how areas are integrated 

mechanically, with Henrici’s explanation . . . . . .51 

Mechanical Integrator by the author, applied to power-measuring machines . 58 

[The steam engine power integrator of Boys] ...... 61 

Example of application of planimeter to diagram from model-ship dynamo¬ 
meters, Admiralty experimental works ...... 63 

The earliest application of the area method for finding the 
product of force X space is due to Southern, who invented the 
Watt-Southern steam engine indicator (Fig. 10), which is the 
parent of all steam engine indicators, such as the “ Dark,” or 
the “ Crosby ” Indicator. In the Southern apparatus a card 
is moved to and fro at a speed proportional to that of the 
piston-rod, while ordinates are drawn by a pencil, attached to 
the end of a small piston-rod, raised against an antagonistic 
spring, by the pressure of steam in the cylinder. In the 
original indicator of Watt (Fig. 11) a needle was deflected over 
a divided dial, and by this means the vacuum produced was 
found. In Farey’s important “ Treatise on the Steam Engine,” 
London, 1827, Southern is mentioned : “ The calculations 

which were required for proportioning the dimensions of 
engines were commonly intrusted to Mr. Southern, who was a 
skilful mathematician, and to whom Messrs. Boulton and Watt 


45 

46 
46 

46 

47 
47 

49 

50 




PLANIMETERS, ETC. 45 

were induced to give an interest in their manufacturing chiefly 
on that account.” 

Recording Apparatus used in Conjunction with Work¬ 
measuring Machines. 

The earliest recording apparatus employed for this purpose 
was that of General Morin, 1841, “ Notice sur divers Appareils 




Fig. 10. 


Fig. 11. 


Dynamometrique.” This apparatus gave the sum of the 
values of the power transmitted by a dynamometer during any 
given period. Since the time of Morin many mechanical 
integrators have been devised for effecting the same summation. 
Experience, however, has taught the investigator who employs 
the dynamometer that a knowledge of the way in which the 
power is transmitted is far more instructive than finding at 
the end of a test the sum of all the elements of the power 












46 


DYNAMOMETERS 


transmitted. In the apparatus of Morin a metal disc rotates on 
an axis, at a rate proportional to space through which the force 
acts ; a small roller about one-fifth of the diameter of the disc 
is carried on an axle, parallel to the surface of the disc and 
cutting its axis. The roller can be slid along the surface of the 
disc in contact with it, so that its point of contact may be at 
any distance from the centre of the disc. This distance from 
the centre is made always proportional to the force acting. It 
will be seen in what follows that the revolutions of the roller 
are proportioned to both the space through which the force 
acts and also to the force and therefore to their product or to 
work . (See note on General Morin.) 

In the continuous steam engine indicator of Ashton and 
Storey the same combination of disc and roller is employed. 
The radial position of the roller is caused to be proportional to 
the steam pressure, while the motion of the disc is due to the 
traverse of the piston ; when the roller is at the centre of the 
disc it does not rotate, and is at a point corresponding to the 
atmospheric line of an ordinary indicator diagram. When by 
virtue of steam pressure the roller is carried from the centre of 
the disc it is made to rotate with a velocity proportional to the 
pressure and also proportional to the velocity of motion of the 
piston of the engine. The principle assumed is that the revo¬ 
lutions of the roller are directly proportional to the work done 
by the engine in a given time. 

In another kind of registering apparatus a band of paper is 
moved by means of a cylinder or cylinders at a rate proportional 
to the space through which the force acts, and ordinates pro¬ 
portional to the force acting are continuously drawn by a 
scribing point. Thus the area generated is proportional to the 
product of force and the space through which it acts, that is, 
to work . 

This method of producing a trace is of great value, since 
it shows at each instant the amount of force acting. In a 
dynamometer made from my designs and shown at the Elec¬ 
trical Exhibition in Paris in 1881, the record was made on a 
paper-covered cylinder, and when the machine was subse¬ 
quently used to test the power absorbed by a loom the work 
elements due to the acceleration of each piece of the mechanism 
in each complete cycle were clearly shown. The trace at once 


PLANIMETERS, ETC. 


47 


suggested that careful balancing of the elementary links or 
parts would reduce the power required to drive the machine. 
In the experimental ship-model tests as now made by the 
Admiralty at Haslar, and also by several of the foreign Powers, 
the diagrammatic registration of power, due to William 
Froude, is always employed. Recently, in 1907, the same 
method of recording power has been used in the torsion-meter 
as applied to ship propulsion by Mr. A. Denny and Mr. 
Edgecombe. The contrast between the behaviour of the 
reciprocal steam engine and the turbine was clearly shown by 
the diagrams, which proved themselves to be very instructive ; 
in fact before this admirable method of recording the trans¬ 
mission of power was employed, what was really taking place 
between the engine and the propeller w r as almost unknown. 
In Germany good work has been done in the same direction 
by Frahm. A description of machines for measuring the power 
absorbed by propellers will be found under the heading 
“ Torsion-Meters. In the figures belonging to the description 
of torsion-meters facsimiles of original diagrams are shown. 

In the work-measuring machines made from the author’s 
designs in 1881-82, in addition to diagrammatic apparatus 
two mechanical integrators were employed. Fig. 12 shows 
the construction of a ratchet and link integrator by the author. 
LK is a link vibrating about the point M. A connecting-rod 
from the ergometer attached at K moves it to and fro, or it 
may in practice be driven much faster than the ergometer 
pulleys by means of intermediate gearing, so that its vibrations 
are proportional to the revolutions of the pulleys. The 
T-shaped piece S is controlled in its movement by the spring 
of the ergometer. Motion in the direction of the arrow would 
result from the extension of the spring. To this T-piece the 
piece H is attached by means of a rolling contact R. E is 
connected by the same device at R', the piece H is connected 
to F by a pin which slides in the link L. The piece E works 
the two arc-shaped pieces CD. These are furnished with 
pauls acting in opposite directions. The ratchet-wheels are 
denoted by the inner circles ; the outer ones denote cog-wheels 
in gear at their point of contact. It is evident that whichever 
way E moves it will be driving round the wheels AB. These 
wheels drive an ordinary recording train of wheels. The arc- 


48 


DYNAMOMETERS 


ended pieces H and F are used so to connect the systems 
together that the effect is the same as if connecting-rods of 
infinite length were used. The ratchet-wheels used in the 
instrument are small pulleys faced with leather, and the pauls 
consist of a small bundle of steel wires ; by this means at 
whatever position the paul is it at once engages with the 



wheel to be driven, and consequently there is no loss of time 
in the action. 

In another integrator I used a small cylinder and piston 
acting as a pump, which raised either water or oil into a 
measuring vessel. Its role of action is analogous to that of the 
integrator just described. The stroke of the pump was made 
always proportional to the force acting, and the number of 
strokes to the distance through which the force acted, so that 
the* quantity of liquid delivered in a given time became a 




























PLANIMETERS, ETC. 


49 


measure of the work clone in that time. The little pump was 
double-acting, so that the flow was practically continuous. 

The area of figures in a plane is found thus :— 

Let OX, OY (Fig. 13) be rectangular axes, and let any number 
of straight lines be drawn parallel to OY equidistant from one 
another, so that the area is divided into a number of elementary 
areas such as A ; also rectangles may be described each equal 
to an elementary area A. Then the sum of the areas of all 
such elementary rectangles equals the area of the whole figure. 
It is evident that the more numerous the elementary areas, 



the more nearly will their opposite sides equal one another 
and also the length of the corresponding rectangle. 

If the width of an elementary rectangle be Ax, ab some 
distance from 0 equal to x, and y the length of the elementary 
rectangle, the area of this rectangle is y Ax. And the sum of 
all such quantities equals the area of the whole figure. In the 
limit when Ax becomes dx, that is, an infinitely small width, 
the area is represented by 



where the integration has been taken between the ascribed 
limits of x, namely, a and b. If by some apparatus a wheel 















50 


DYNAMOMETERS 


is made to rotate at a rate proportional to the value of y and 
the frame from which it takes its motion traverses OX at a 
uniform rate, the rotation of the wheel will indicate the whole 
area contained by the boundary passed over by the wheel. 

It would be entirely beyond the scope of this book to give 
anything more than a sketch of this attractive subject, but 
sufficient directions will be found for estimating those diagrams 
which are generated by recording dynamometers of different 
kinds. Should the reader wish to study the interesting 
subject of the methods whereby integration has been effected 
by mechanical means, the following papers and references 
may be consulted :— 

“ Amsler’s Planimeter ” : Sir Frederick Bramwell, F.R.S., 
Report, British Association, 1872, pp. 401—412. 

“ An Integrating Machine ” : C. V. Boys, Proceedings of 
the Physical Society of London, Vol. IV., pp. 199—206 ; 1881. 

On “ Integrating and other Apparatus for the Measurement 
of Mechanical and Electrical forces ” : C. Y. Boys, Proceedings 
of the Physical Society of London, Vol. V., pp. 8—29 ; date 
of paper, November 26, 1881. 

“ Apparatus for Calculating Efficiency ” : C. V. Boys, 
Proceedings of the Physical Society of London, Vol. V., pp. 28 
—35 ; date of paper, January 28, 1882. 

“ Analytical Investigation of the Amsler Planimeter,” and 
also a geometrical treatment of the subject, by Prof. Ball; 
see “ Integral Calculus,” B. Williamson, F.R.S., 1884. 

“ Mechanical Integrators,” by Prof. H. S. Hele Shaw, 
Vol. LXXXII., Proceedings of the Institution of Civil En¬ 
gineers, 1884—85 ; p. 92. 

“ The Hohmann-Coradi Precision-Planimeters ” : Pamphlet 
edited by Luckhardt and Alten, Cassel, 1885. 

“ The Theory of the Planimeter ” : Prof. A. G. Greenhill, 
F.R.S., Encyclopaedia Britannica, Vol. XXII., p. 721 ; 1898. 

“ Integrator applied to Dynamometers,” by the author ; 
exhibited Royal Society, 1894. And also description in 
German : “ Deutsche Mathematiker-Vereinigung,” Sonder- 

Abdruck aus dem 1892; “ herausgegebenen Katalog Mathe- 
matischer Modelle, Apparate und Instrumente.” 


PLANIMETERS, ETC. 


51 


The Amsler Polar Planimeter as used by Engineers 
and Ship Builders. 

[The Amsler polar planimeter is a neat instrument which has 
the property of giving directly, by the rotation of a roller called 
an index-wheel, the area of a plane figure when the tracing 
point is carried once round the periphery of the figure. It 
consists of two bars 
jointed to one another 
(Fig. 14), while at one 
end of each there is 
a point one of which 
forms a pivot about 
which the instrument 
may be turned which 
carries a small weight, 
while the other is made 
to trace the outline of 
the figure. The third 
point of support is the 
edge of the index - 
wheel, which is carried 
by the pointer arm 
and so mounted that 
the axis of this wheel, 
the pivot connecting 
the two arms, and the 
pointer lie in the same 
vertical plane. The 
index-wheel and pivot 
are often carried on a sliding frame, which can be clamped to 
the pointer bar at any point and then adjusted accurately by 
means of a micrometer screw, so that certain marks corre¬ 
spond, when the unit of the vernier reading of the index- 
wheel will be a simple number of square millimetres or a 
simple fraction of a square inch or square foot or other unit 
as indicated by figures engraved on the bar.] 

The lowest point on the inclined arm (Fig. 14) is the pivot, 
and the highest is the tracing point. This, which is not sharp, 
is placed on some mark on the boundary of the diagram which 

E 2 




52 


DYNAMOMETERS 


is to be estimated, and the reading of the index-wheel taken. 
Then the tracing point is taken round the boundary till the 
mark is again reached ; the index reading is again taken. The 
difference of the two readings shows the value of the area in 
terms of the selected unit. In order that the instrument may 
be calibrated it is convenient to take the tracing point round a 
known area and note the reading of the index-wheel. This is 
most accurately done by means of a thin metal radius bar of 
known length R ; one end of this bar is pivoted by means of a 
projecting needle stuck into the drawing-board, at a point 
which is roughly the middle point of the area to be found; the 
tracing point of the planimeter is then placed on a small conical 
indentation near the free end of the bar so that it is at a known 
distance R from the pivot. The position of the free end of the 
bar is marked by a fine line on the paper below it and the index - 
wheel read ; then the radius bar, carrying with it the tracing 
point of the planimeter, is rotated once and the reading of the 
index-wheel again taken. The area ttv 2 should be shown by the 
reading of the index-wheel. By very carefully adjusting the 
position of the slide on the tracing bar of the planimeter the 
accuracy of the indicating marks engraved on the bar can be 
tested, or the correct positions determined if error is found. 
The greatest care should be taken in handling the instrument, 
as its excellence of performance depends on the joints being in 
perfect adjustment, that is, free to move without any shake. 

The following are the essential points in the construction of 
the polar planimeter :— 

The pin of the joint connecting the two bars, the axis of the 
wheel, and the end of the tracing point must lie in one plane. 
The roller or wheel must run easily and free of the vernier. The 
roller, which is furnished with a tangent screw, drives a count¬ 
ing-wheel once for every ten turns of itself. The primary 
divisions of the roller are ten in number ; these are again sub¬ 
divided into ten parts, and these are, by means of a vernier, 
again divided into ten parts, so that one thousandth of a turn 
corresponding to the one hundredth of a square inch or corre¬ 
sponding unit can be estimated. It is important that the 
paper on which the diagram to be integrated is drawn is free 
from ribs ; these tend to give the roller a slight rotation when 
moving at right angles to itself, when there should be no 


PLANIMETERS, ETC. 


53 


rotation at all. When a fairly smooth paper is used, practically 
no error is introduced by its surface. 

To use the instrument: set the tracing point to a fine mark 
on the boundary of the area, and it is well to press the point on 
to the paper so as to make a slight indentation which can be 
felt, read the counting-wheel, the roller, and the vernier. Lead 
the tracing point round in the direction of clock-hands until the 
mark is again reached, and take the reading. The difference 
of the two readings gives the area. But two cases have to be 
considered, the first when the pivot is within the area, and the 
second when it is outside it. When it is outside, the difference 
of the two readings has to be taken, but if it is inside the 
area, then the excess of the second reading over the first 
gives the area between a circle of known value, called the datum 
circle, and the boundary of the area. If the figure is less 
than the datum circle, then the result is negative ; therefore 
the area of the datum circle has to be added to the second 
reading before subtracting the first from it—what is over equals 
the area sought. 

It is important that the pivoted bar of the planimeter should 
be so placed that when the tracing point is taken round an area 
the angle between the bars should not be very great or very 
small. When it is so, the tracing point is not quite so easily 
led round the boundary furthest from or nearest to the pivot. 
The position of the planimeter with respect to the area shown 
in the figure would be found to work well. 

The planimeter when well manipulated gives such valuable 
results that it will well reward the user to learn its different 
applications by careful practice. Before planimeters were 
invented, areas were found by the method devised by Simpson. 
His rule is exact for parabolic figures of the third degree, but 
for other figures it only gives the approximate area. The 
method is interesting and instructive, but requires careful 
construction and working to obtain good results. Examples of 
its application are given at pp. 63—66, “ Rules and Tables,” 
by W. J. M. Rankine, F.R.S., 1876. 

Theory of the Polar Planimeter. 

In order that the area or the mean force line may be found 
from an ergometer diagram, an instrument whereby the area 


54 


DYNAMOMETERS 


is found at once by moving a tracing point round its boundary 
line, is usually employed. The following explanation of the 
planimeter of Amsler, which is much used in the office of the 
engineer and shipbuilder, is based on notes taken by the author 



B T c 



T 

r> v 

l< 

X 

P ~ * 

w 


A Q D 


at a lecture on the subject given by Prof. 0. Henrici, F.R.S., 
many years ago. 

The construction of the Amsler-Laffon * planimeter is 
shown diagrammatically in Figs. 15—21. The radius bar OQ 




and the pole arm QT are hinged at Q ; the bar rests on a hori¬ 
zontal plane, such as paper attached to a drawing board, on 
three points, viz., the tracing point T, a point of contact of a 

* In the year 185G Prof. Amsler-Laffon invented the polar planimeter called 
after him. Up to 1885, 12,400 of these instruments were sent out of his works at 
Schaffhausen : Vol. LXXXII., Proc. I.C.E., p. 14. 











PLANIMETERS, ETC. 


55 


small wheel W, and a sharp point 0, round which the system 
is free to rotate while T is moved on the boundary line of any 
area, the value of which is sought in terms of some unit of 
square measure, such as the square inch or square centimetre. 
We may first consider the pole arm of QT and the wheel W 
apart from OQ. The axis of the wheel is so placed that it 
lies in a straight line passing through vertical lines through 
Q and T. 

Let TQ — l (Fig. 16), AD = p, and let the initial position 
of TQ be AB ; suppose it to move parallel with itself, from BA 
to CD, then the area Ip is swept out. Now p equals some 
multiple of the circumference of the wheel W. Calling this 
w, p — w and the area A = Iw. Suppose the circumference 
of W to be divided into n equal parts, 
each very small and = u, then w 
equals the number of all the u 
quantities rolled over, and w gives 
the sum of the elementary areas lu 
contained in the rectangle. Any 
unit may be employed by duly 
arranging the length l and the radius 
of the wheel W. 

Next let the rod (Fig. 17), i.e., the pole arm, rotate about Q ; 
it will then sweep out an area =s \ l 2 d, where d is the circular 
measure of the angle AQB. The wheel rolls over the arc cQ, W 
being placed c units from Q ; therefore w = c9, and the area 
l 2 

= | - w, so that w shows the value of the area swept out. 

Next let us suppose the rod (Fig. 18) to move parallel to 
itself but not in a direction perpendicular to itself. When this 
is the case the wheel both rolls and slips. Let the rod QT 
move through a small space to Q'T'; this can be resolved into 
a motion perpendicular to the rod, which would bring the rod 
to RR', when the rectangle QTR'R would be generated, and the 
sliding of the rod along its own axis from RR' to Q'T', this second 
motion not generating an area. In the first movement the 
wheel’s rotation would give QR, and during the second motion 
the wheel would not rotate. The rotation of the wheel thus 
gives the value of the area QTT'Q'. Now (Fig. 19) suppose the 
motion of the rod to be made up of small steps all resolved 


D 





56 


DYNAMOMETERS 


in a similar manner, then the rotation of the wheel shows 
the generated area as before. Again resolving the motion 
into a large number of small steps let AB move to CD, the 
step being considered so small that the arcs AC, BD may be 
taken as straight lines. The area swept out is ACDB ; this 
motion can be resolved into a step from AB to CB' parallel 
to AB, and a rotation about C, from CB' to CD. Then the 
rotations of the wheel W when summed up give 
w — p + c9. 

W is distant, as before, c units from A, and the total area 
A swept out is 

A = lp + l l 2 6 , 

p being expressed in terms of w. 

For finite motion the whole area equals the sum of the areas 
swept out during the different steps. But since the wheel 
continuously rolls, the total rotation will be the sum of all the 
successive elementary rotations. If the whole rotation be 
called w, if the sum of all the small turnings 6 be called a, 
and the area A, then 

A = lw+(±l 2 -lc)a; 

a is also the angle which the first and last positions of the rod 
make with one another. 

When the planimeter is used, the rod QT is always brought 
back to its initial position, so that a = 0, or should the rod be 
turned once entirely round a = 2n. 

In the first case A = lw 
In the second case A = Iw -j- ( \l 2 — Ic) 2n, 
when the rod is turned round once. 

Since the point Q in the first case only moves to and fro 
on an arc of a circle, no area is generated by it. But in the 
second case, if the pole 0 be situated within the area, the 
rod QT describes the area between the boundary of the figure 
and the circle having a radius r equal to OQ, and the rod 
turning once round makes a = 2tt, so that in this case the total 
area A 

A = Iw + (\l 2 — Ic ) 277 + vr 2 
or =lw - j - C where C = (| Z 2 — Ic) 2tt + nr 2 , 

a constant depending on the dimensions of the instrument, 
which will be found marked on one of the bars. Where several 
standard positions are marked on the tracing bar representing 


PLANIMETERS, ETC. 


57 


different units, corresponding constant values will be found 
given for each. 

[It may be well to add that where the index-wheel is placed 
beyond the hinge Q, as is usual in instruments in which the 
hinge and wheel are carried on a sleeve itself capable of sliding 
on the bar TQ, so as to read square feet, square inches or 
square millimetres or other unit according to the mark to 
which it is set (Fig. 14), the term — Ic in the preceding equa¬ 
tions should be + Ic. It will be evident that if the point T is 
carried round the pole 0 in a circle of such size that the wheel 
does not roll at all, the plane of the wheel will pass through 
the pole. 



An inspection of Figs. 20 and 21 will then show that p, the 
perpendicular distance from the pole to the wheel, r, the length 
~of the pole arm, and R are the radii of three circles described in 
this movement; also that 

p 2 = r 2 — c 2 

R2 = p2 + (i± c y 

==r 2 ± 2 cl + l 2 , 

and the area of the circle of radius R described by T — 
77 -(r 2 ± 2d + l 2 ), which is the same as is given above. Of this 
7 tt 2 is the area of the circle described by the joint Q while 
ttX 1 ± 2ird is the area swept by the radius rod l outside the circle 
described by Q. That part of the radius rod which is within 
this circle in Fig. 20 sweeps over it twice, once positively and 
once negatively, and this does not count.] 






58 


DYNAMOMETERS 


Mechanical Integrator. 

Mechanical Integrator used in connection with the Ergometer. 

A metal cylinder AB is carried on an axle CD (Fig. 22) which 
rotates in a frame suspended from a steel rod, which moves in 
two V-grooved pullies (see Fig. 23 and picture from photograph). 
The frame is connected to a double-grooved semicircular 
disc Q, which forms part of the frame FH which carries the 



hemisphere, by two cords ; this keeps the cylinder always in 
rolling contact with the hemisphere when turned through an 
angle about its vertical axis ; a counter attached to the axle of 
the cylinder shows the number of revolutions it makes, and 
hence, as will be shown, the work transmitted by the machine. 

The horizontal motion is given to the hemisphere through 
the arm carrying the stud E (Figs. 23 and 24) and frame LH 
which is attached to the arm, a continuous cord passing round 
a V-groove on a great circle on the hemisphere, and through its 
vertical axis rotates the hemisphere. Thus the cylinder and 




















PLANIMETERS, ETC. 


59 


hemisphere are in perfect rolling contact when the hemisphere 
is moving about either axis, separately, or about both axes at 
the same time. The stud P (Fig. 22) moves in a slot ST, 


JT 




carried on a geometric slide having five surfaces of contact, 
shown in a side view, WV. The length MP (Fig. 22) is propor¬ 
tional to a force when the instrument is used in connection with 
ergometers. The theory of the instrument is as follows :— 

If the rod FE (Fig. 22) is pushed through a distance y, then 













































60 


DYNAMOMETERS 


the hemisphere moves through an angle 9 about its vertical 
axis, so that a sin 9 = y, where a is the distance from the centre 
of the hemisphere to the stud P. Since the hemisphere and 
cylinder are in contact, and c = radius of cylinder, and 

R = r sin </>=-?/, and r = radius of hemisphere, we have cdd = 
ct 

Rd</r, where di/j is the angle turned through by the hemisphere 
on its horizontal axis, and dd the angle turned through by the 
cylinder so that we get 

dd = —ydy\f 

Q/C 

Since the revolution of the hemisphere is caused by the cord 
which engages in the V-groove in the hemisphere, the angle dip 
is proportional to the motion dx through which a point on the 
cord has moved, so that dd = A ydx, 



where A and B are constants depending on the dimensions of 
the instrument. 6 is measured by means of a dial on the axis 
of the cylinder. 

The instrument is used in connection with a work-measuring 
machine shown in the photograph, and it is so mechanically 
arranged that x is proportional to the space, and y to the force 

acting through the space x, so that j* ydx gives the work 
transmitted by the ergometer. 

For many purposes the mechanical integrator is of consider¬ 
able value, but when fluctuations in the rate of transmitting 
work take place, then the best method for obtaining the value 
of the work transmitted is from a diagram produced auto¬ 
matically on a cylinder carrying paper, in which the traverse 
of the paper is proportional to the distance through which the 
force acts, and the ordinate is proportional to the force at any 
instant. The area then gives the value of the work transmitted. 
In testing machines in which periodic motion exists, such a 
diagram shows continuously how the work is transmitted. In 
one form of my ergometers used in testing spinning machinery 
(at Messrs. L. Crossley’s, Halifax) the diagram method is 
always used, as it shows at what rate any particular part of 
the machine is absorbing energy. The different moving parts 


PLANIMETERS, ETC. 


61 


are connected electrically with electromagnetic styli which 
mark the diagram, so that the behaviour of each part is clearly 
indicated. 

The torsional form of ergometer has been in continuous use 
for the last two years in the Millard Mechanical Laboratory, 
in connection with the experimental determination of the 
mechanical equivalent of heat from the rotation of copper 
cylinders in the magnetic field. 


Boys’s Engine Power Meter. 


[Boys’s Engine Power Meter was mentioned in the table of 
contents prepared by the author, but he had not written any 
description of it. This instrument depends on the principle 
employed indepen¬ 


dently by Abdank 
Abakanovicz, and 
C. V. Boys in their 
integraphs. If while 
a point P is made to 
trace any given curve 
AA (Fig. 25) a steering 
wheel W is by some 
means always kept 
vertically above the 
point P and parallel to 
the line PQ, the base 
QM being maintained 
constant, then the 
wheel W will trace 
out a curve such that 
the tangent of its in¬ 
clination is numeri¬ 
cally equal to the 
height PM if the base 
QM is unity. The x 
curve BB therefore 
gains in height in pro¬ 
portion as the area 
between the curve AA 
and the axis of x gains 



x 


Fig. 25. 







62 


DYNAMOMETERS 


in area, and the process is a mechanical realisation of mathema¬ 
tical integration. The curve AA in Fig. 25 represents the com¬ 
bined indicator diagrams of a steam engine taken at the two ends 
of a cylinder and the curve BB traced by the steering wheel W is 
the integral curve. It will be seen that on the return journey 
from right to left the slope of the line QP is reversed in direction 
also, and the steering wheel W having its direction of motion 
and slope both reversed, continues to mount, thus adding the 
area below the line xx to that above the line. The height BB 
of any one zig zag X QM = area enclosed by the curve AA. 
In order to make this construction practicable as a steam power 
integrator an ordinary indicator cylinder is used with the two 



ends put into communication with the two ends of the steam 
cylinder of the engine. In the place of one double-acting 
instrument two single-acting instruments may of course be 
used one connected to each end of the steam engine cylinder. 
Considering now the double-acting instrument, the upper end 
of the cylinder is seen in Fig. 26 of which the left hand part is a 
vertical cross section through the broken line aa, while the right 
hand part is a side elevation with the cover only in section. 
The piston rod of the indicator is seen with the indicator spring 
above the cylinder connected to the piston-rod, so that the dis¬ 
placement of this above or below its neutral position is propor- 



































PLANIMETERS, ETC. 


63 


tional to the excess of pressure on one side of the piston over that 
on the other. The upper end P of the piston-rod is in the form of 
a swivel sleeve engaging a rod, which projects radially from a 
bell within which the wheel W is free to rotate, and the bell 
with its wheel W is turned more or less by movement of the 
piston-rod, so that the tangent of the inclination of the rod and 
of the wheel W is proportional to the displacement of the 
piston-rod. The bell is pressed by the action of a spring 
towards a light drum C against which the wheel W is pressed, 
and this drum is given a reciprocating movement in time with 
and proportional to the motion of the piston of the engine by 
means of a flexible connection acting against a spring in a 
manner made clear in the figure. The hemicylindrical case 
containing the integrating mechanism can be turned upon the 
cylinder so that the flexible connection points in the desired 
direction and it may be locked in that position by means 
of a union nut. When the integrator is working the 
wheel W is inclined in accordance with the steam pressure, 
while the drum C is drawn under it in conformity with the 
motion of the piston of the engine. The wheel is unable to 
move vertically as in the integraph, but the surface of the 
drum is free to move under the wheel instead, and so it rotates 
at any moment at a rate proportional to the product of the 
effective pressure multiplied by the speed of movement of the 
engine piston, i.e., to the rate at which work is being performed 
by the steam on the engine piston, and the whole rotation of 
the drum C transferred by the axle A, on which it slides with a 
feather connection, to a counter in the box at the left-hand 
end gives on a set of dials there the integrated indicated work 
of the engine over any length of time. A hemicylindrical cover 
springs on and protects the integrating mechanism. Unlike 
the power meter of Ashton and Storey, there is no sliding 
between the integrating surfaces of this integrator. If the 
spring is not the exact length needed to bring the wheel W into 
its neutral position when the piston is unacted on by steam 
pressure, the record due to any complete number of strokes is 
not affected, as the tangents of the inclinations of the wheel W 
will be increased during alternate strokes to the same extent 
that they are diminished during the intermediate strokes. It 
will be seen that if 


64 


DYNAMOMETERS 


D is the diameter of the engine cylinder ) in the same 

d ,, diameter of the indicator cylinder j units 

L „ stroke of the engine piston ) . ,, 

7 ’ , , 7l . ® j i [ in the same units 

l „ stroke of the integrator drum J 

S ,, stiffness of the spring, i.e., ten times the number of 

pounds required to move it one-tenth of an inch 

K is the distance in inches between the axis of the piston- 

rod and the centre of the wheel W 

r ,, radius of the drum C in inches 

n ,, number of turns of the shaft A recorded in the 

counter 

, number of foot-pounds of indicated work 


N 

then 


, T D 2 L ~ T7 . nnr 

N = # x t xSKx it 


The coefficient of n may be determined once for all; calling 
this k, then N = kn.] 

As an example of the use of a planimeter in dynamometry 
the reduced trace (Fig. 27) is given. This is a dynamometer 
record taken during an experiment on a model ship drawn 
through water in a testing tank. The traces showing the large 
oscillations exhibit the force required for towing the model 
ship. The traces which are rather darker, showing smaller 
oscillations, exhibit the thrust of the propeller. The top 
broken line shows the revolutions per minute of the screw. The 
middle broken trace shows the distance traversed, viz., 25 feet, 
between each break, also the lowest broken line shows the 
revolutions per minute of a screw. The horizontal lines ruled 
through the traces show different values of the mean forces 
involved. 

For example, in a diagram taken from a model ship-testing 
ergometer the following numerical values were obtained :— 

The force = 3-5 pounds, and it acted through 25 feet, so the 
work done = 3*5 x 25 = 87-5 foot-pounds. The space 25 feet 
was represented by 1-83 inches on the diagram,* while the load 
of 3-5 pounds was represented by 8-9 inches so that an area of 
the diagram of 8-9 x 3*5 = 16-189 square inches represented 
87*5 foot-pounds work done, and one foot-pound of work was 

represented by =■ 0T8512 square inch. 

o7 *0 


* The figure is reduced from the original diagram. 



PLANIMETERS, ETC. 


65 


Periodic Curve and Record . 

In many ergometer tests the diagram shows a well-marked 
periodic curve. This is very evident when the force acting is 



d. * 






























66 


DYNAMOMETERS 


with a diagram of this kind, a mean line of force is found 
and at once multiplied by the space through which the 
force has acted. The operation for finding this mean line is 
that of integrating the area of the diagram between convenient 
limits and dividing the area so found by the length of the base 
line. Or another method is to draw a mean line by eye, cutting 
each wave of the curve, and then integrating with a planimeter, 
such as that of Amsler or Coradi, the whole surface bounded by 
the curve, half of which lies roughly above the assumed mean 
line and half below it. If after traversing a length of the curve 
containing an equal number of crests and hollows and returning 
by the assumed mean value line to the starting point, the read¬ 
ing of the planimeter is zero, this line has been correctly drawn, 
but if some small area is indicated, then the line must be shifted 
through the distance deduced from the reading ; it will then 
become the mean value of ordinate line. 

In certain cases, such as the towing of a vessel, through an 
ergomometric apparatus, the band of paper used for recording 
the force ordinates cannot be driven at a rate directly propor¬ 
tional to the space through which the force acts, but is driven 
continuously forward by means of clock-work regulated by a 
centrifugal governor of the type in which a spring control takes 
the place of gravity. But it must be noticed that the record 
so made is of impulse , Ydt, not of work , Fds. If the 
quantity, F dt, be divided by the whole time that F acts, the 
quotient will give the mean value of the force F, but if under 
this condition work is to be estimated, then as the ship passes 
known distances, determined by shore marks, the position 
must be marked on the diagram at these points at each instant 
they are passed and the mean force estimated between them. 
Then by multiplying this mean force by the distance between 
the marks an approximate value of the work during the interval 
is obtained. 


CHAPTER IV 


FRICTION BRAKES 

Some Applications of Coiled Ropes. 

Some early applications of coiled ropes (Homer) 

Bollards and hawsers ..... 

Resistance due to coils of rope on a cylinder .... 

Sir Christopher Wren’s “ Engin ” . 

The rope dynamometer brake....... 

Equation for the rope brake ....... 

W. Thomson s (Lord Kelvin) application of the coiled rope as a dynamometer 
brake ......... 

Abstract of Thomson’s patent: This brake invented in connection with 
laying the Atlantic cable. 

W. C. Unwin’s dynamometer ...... 

Society of Arts motor trials, use of the rope brake . 

Modification of Thomson’s brake by Capt. Sankey 

Rope brake at the City and Guilds Technical College, London 

Friction brake, formerly at Cooper’s Hill College, showing method of cooling 

Dynamometers by James Thomson 
» „ Imray 

„ ,, Carpentier 

,, ,, Raffard 

,, „ Reckenzaunn 

„ „ Scheibe 

Block Brake dynamometers by Prony 
„ „ Coope 

,, ,, Appold and Amos 

,, ,, Balk . 

,, ,, Garret and Sons (water-cooled brake wheel) 

„ ,, [Griffin Engineering Co., Ltd.] 

[Alden dynamometer] ...... 

[Nicholson lathe tool dynamometer] 


PAGE 

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73 

73 

75 

76 

77 

78 
80 
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85 

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86 
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89 

90 

90 

91 
93 
93 


In very remote times it was well known that a spindle might 
be rotated by means of a thong or rope coiled about it. In the 
adventure of Ulysses with the Cyclops (Homer, “ Odyssey,” 
IX.), Ulysses, assisted by his companions, when in the cave 

F 2 







68 


DYNAMOMETERS 


of the Cyclops bored out his eye with a bar of olive wood, 
“ having bound it with a thong on each side, they move it, and 
it constantly runs round.” Ulysses after chaffing the blinded 
Polyphemus, the Cyclops, in polite and polished Greek, escapes 
from the grasp of the monster while clinging to a fat ram going 
out to pasture as the rosy-fingered morn dawned. In the 
earliest lathe the material held between points was rotated to 
and fro by means of the cord of a bow coiled at least once 
round it. It was so in the time of Virgil, and it was probably 

used in the same manner ages 
before his time. 

The use of the coiled rope 
must have been known to sailors 
long ago, who moored their 
vessels to trees or short posts 
projecting from the wharf. Such 
posts have led up to the iron 
bollard, in some cases of enor¬ 
mous size, so that a steel rope 
may be coiled round it. If a 
flexible cord be coiled round a 
cylinder as shown in Fig. 28, and 
weights be attached to its ends, 
the friction of the cord increases 
greatly with the angle embraced 
by it. Suppose that the cord 
embraces half the circumference, 
and the relative value of the two weights be such that the 
greater weight is balanced by the lesser one plus the friction 
of the cord on the cylinder. If we assume that the mean 
value of friction as about one-third, or more nearly -35, of the 
pressure which causes it, then any weight tied to one end will 
support a weight at the other end three times as great. 


Coils. 

Weight. 

Coils. 

Weight. 

0-5 

3 

2-5 

243 

1 

9 

3 

729 

1-5 

27 

3-5 

2,187 

2 

81 

4 

6,561 



Fig. 28. 




















FRICTION BRAKES 


69 


When another coil is taken round the cylinder the small 
weight will carry one twenty-seven times as great, and each 
coil multiplies the friction roughly nine times, and also the 
half-coils three times. It will be noted that half a coil neces¬ 
sarily forms part of the sum of all the coils. 

If the small weight be raised a little so as to release the half- 
coil slightly from the cylinder, the greater weight will descend, 
but if the small weight be again allowed to act it will be brought 
to rest. This is true, too, when a ship is warped to a bollard ; 
a slight release of the slack end of the rope enables one man to 
control with ease the paying out of a rope, which has a great 
pull on it due to a ship in moving water. This property of the 
coils of a rope is utilised in such devices as hand-gins for raising 
or lowering builders’ materials, and also in raising and lowering 
buckets alternately into a well. In this case the empty bucket 
corresponds to the small weight and the full one the large 
weight previously mentioned. This way of using the coiled 
rope is inconvenient when the well is deep, since the lateral 
movement of the rope as it coils on to the cylinder is limited 
by the width of the well. An invention of Sir Christopher 
Wren is so excellent that I give a verbatim reproduction of it 
from the Royal Society, May 5, 1670 :— 

“ Having considered, that the ways hitherto used in all Engins for 
winding up Weights by Roaps have been but two, Viz. the fixing one 
end of a Roap upon a cylinder or Barril, and so winding up the whole 
coyle of roap ; the other by having a Chain or a loose roap catching on 
teeth, as is usual in clocks ; but finding with all that both these waves 
were inconvenient the first, because of the riding of much roap in 
winding one turn upon another ; the other, because of the wearing out 
of the Chain or roap upon the teeth, I have, to prevent both these 
inconveniences, devised another, to make the weight and its counter- 
poyse bind on the cylinder, which it will doe if it be wound three times 
about. But because it will then in turning, scrue on like a worm, and 
will need a Cylinder of very great length, therefore if there be two 
cylinders, each turned with three notches and the notches be placed 
alternately, the convex edges to the concave as in the figure adjoyned, 
the roap being wound three times about both cylinders, will bind firmly 
without slyding and working up the weight with a proportionable 
counterpoyse at .the other end of the Roap.” 

The original picture (Fig. 29) in Wren’s paper is not very 


70 


DYNAMOMETERS 


clear, so I show a reproduction of it from 44 Principles of 
Mechanism,” 1870, by R. Willis, M.A., F.R.S., Jacksonian 

Professor of Natural 
and Experimental 
Philosophy in the Uni¬ 
versity of Cambridge, 
by the kind permission 
of Longmans, Green 
& Co. (Figs. 30 and 

31):— 

“ The course of the cord 
is over the back roller from 
A to B, under the rollers 
at BC, and over them at 
CD, and so on to E,F,G, 
over at GH, but after 
passing under H the end 
of the cord is taken,, not 
under, but over at I, 
whence the end is allowed 



Fig. 29. 


to hang down vertically, and has a small weight tied to it of suffi¬ 
cient magnitude to keep the cord in contact with the surface of the 
notch.” 




By means of this excellent combination of the grooved 
cylinders the ends of the cord which carry the load and the 



































FRICTION BRAKES 


71 


counterpoise hang in vertical lines when the machine is at work 
and the frictional resistance due to several coils is effectual. 
The sum of the frictional resistances of the rope in passing 
round the two halves of the two cylinders is the same as if it 
was coiled the same number of times round one cylinder, so 
that both the increase of diameter due to successive coils and the 
lateral motion of the hanging ropes is entirely avoided. This 
excellent device, as an invention of Wren, appears to have 
been lost sight of, and reinvented by several persons, M. 
Boulogne in 1702, J. Bernouilli and Ludot in 1741, and in 1805 
the Society of Arts rewarded Boswell for a similar invention. 
The same device has been applied to produce reciprocation of 
motion as required in a mangle. It will be seen in what 
follows that it is on the property of the coil friction of ropes 
that the excellence of a certain class of brakes depends. 

This method of coiling the same rope round several cylinders 
has also been turned to good account in one form of the rope 
brake of William Thomson (Lord Kelvin). 

The Rope Dynamometer Brake. 

In this type of brake a rope is coiled once round a pulley or 
flywheel driven by the engine to be tested. A weight W is 
suspended from its lower end ; and its upper end is attached 
to a spring balance of the Salter type. The direction of 
rotation is such that the rim moves upwards on the side where 
the ends of the rope are situated. The spring balance can be 
so adjusted that the rope may hang in a vertical line when 
touching the wheel of the engine. For all practical purposes 
this is a sufficiently good approximation to the real physical 
condition of a rope in contact with a curved surface. Owing 
to the fact that the rope is not really perfectly flexible, it 
cannot hang in a direction truly tangential to the curved 
surface, so that there is a tendency inherent in the rope to 
make the efficient radius at which the forces act slightly larger 
than it is usually assumed to be. In the case of a small pulley 
embraced by a rope of considerable diameter this increase 
could not rightly be neglected. If instead of a quasi-flexible 
rope a chain such as those used in the cycle be used, each 
link being faced with a suitable rubbing surface, a condition of 


72 


DYNAMOMETERS 


brake could be set up which is almost absolutely free from the 
minute source of error introduced by the employment of a rope ; 
but this increase of accuracy appears in practice to be more 
than balanced by other troubles introduced by the employment 
of a steel chain with faced links. When more than one rope 
is employed they are kept in place by distance-blocks of wood 
arranged to prevent side slip No metal, if used to attach the 
blocks to the ropes, should come in contact with the face of the 
wheel, since such contact produces great and dangerous heating. 
If R is the distance between the perpendicular let fall through 
the centre of the wheel and a parallel line through the centre of 
gravity of the weight, we have two reacting moments, namely, 
the force of friction / acting at the radius r of the wheel and the 
effective weight (W — p) acting at the distance R. p is the 
pull shown on the Salter’s balance, when the wheel is rotating 
at the required speed of N revolutions per minute and 
fr = (W -p) R 

the BHP ^ 7r (W p) RN 

the E.H.E.- 330 do- 


tt = 3-14159 and 33,000 is Watt’s Horse Power constant. 

If /jl (the coefficient of friction) changes, then W changes its 
position until the reaction becomes steady. It has been already 
W 

shown that — = e^ e , where 9 is the angle in radians embraced 
V 

by the rope and e = 2-71828. In the case described, since 
the rope entirely embraces the wheel, 6 = 2tt. 

W 

As 9 increases — increases quickly, so that if 9 is large p may 

be a small fraction of W, and consequently the small errors in 
estimating the readings of the spring balance are not of great 
importance. 

The governing power of this brake is excellent, and it can be 
easily applied and used in estimating the brake horse-power of 
many kinds of motors or prime-movers. The brake used as a 
dynamometer is thus described by William Thomson in his 
patent No. 437, a.d. 1858. 


“ Part Fourth. I use the arrangement which has been described for 
the purpose of testing the action of water wheels, steam engines, and 
other prime-movers. In performing this part of my invention I employ 



FRICTION BRAKES 


73 


the prime-mover to drive a rotating body resisted by the friction of a 
band, which is held at the end or part where the tension is greatest by a 
regulated force, and at the end or part where the tension is least by a 
spring balance or other indicator of force. The difference between the 
regulated force and the force indicated by the spring balance or other¬ 
wise is the resistance overcome at the rubbing surface of the rotating 
body, which, being multiplied by the velocity of that surface, gives the 
work performed in a given time.” 

When a very thin friction band is employed, the difference 
between r and R for a wheel of considerable diameter is so 
small that it may be neglected. 

The Rope Dynamometer Brake of William Thomson 
(Lord Kelvin). 

The patent specification of William Thomson, No. 437, 1858, 
for improvements in apparatus for applying and measuring 
resistance to the motion of rotating wheels, shafts, or other 
rotating bodies, is so full of valuable matter relating to brakes 
that I give here a brief analysis of it. 

In the experiments made by the Society of Arts, 1888—89, 
the Thomson brake was employed, but its inventor appears to 
have been forgotten. Probably the apparatus would now be 
better known if some diagram had been added to the specifica¬ 
tion, which is tersely written, and more academic in its wording, 
than is usual in patent specifications of more recent date. The 
matter contained in the specification may be described thus. 
A flexible band is wrapped round any part of the circumference 
of the pulley which is driven by a prime-mover, and it may be 
wrapped round it one or more times. To one end of the band 
a regulated force, i.e. a weight, is attached, which opposes the 
motion of rotation, and to the other end a spring balance is 
attached. The adjustable weight is applied where the tension 
is greatest, and the tension at the other end is left to vary with 
the change of friction, so that by this arrangement the resistance 
cannot exceed the amount of the force due to the adjustable 
weight. If the adjustable force due to the weight were applied 
to the end where the tension is least the resistance might increase 
beyond that of the adjustable force, and irregular motion 
would result, or the sudden stoppage of the rotating body. 


74 


DYNAMOMETERS 


The band is in some cases wrapped round the whole or any 
portions of the circumferences of a number of different pulleys, 
moving on parallel axes, geared together or not, or it may be 
wrapped round one of these pulleys more than once, one end 
being acted on by the adjustable force before mentioned, and 
the other end is either fixed or attached to a spring balance, 
indicating the tension. This arrangement is designed to 
resist the motion of different pulleys to an amount which may 
be modified by regulating the forces at each end of the band. 



The brake described was to be employed in setting up resistance 
opposed to the egress of a cable. In order that the rubbing 
surfaces might be renewed without stopping the pulleys, a band 
is used longer than that absolutely required, and this is gradu¬ 
ally paid out so that new surfaces may be successively exposed 
to friction, also new surfaces of the pulleys may be exposed to 
friction. 

The invention is also designed to test the action of water 
wheels, steam engines and other prime-movers. The prime- 
mover is employed to drive the pulley, the motion of which is 
resisted by a rope coiled on it, one end where the tension is 



























FRICTION BRAKES 


75 


greatest being subject to an adjustable force (due to a suspended 
weight), and the other end, where the tension is least, to a 
spring balance or force indicator (Fig. 32). The difference 
between the force due to the weight and the force indicated by 
the spring balance is the resistance overcome at the rubbing 
surface of the rotating body, and this multiplied by the velocity 
of the surface gives the work performed in a given time. 

In each case of the application of the friction band or rope 
to a pulley springs may be attached at different points, and so 
adjusted that when no tension is applied to the band, it is 
drawn out of contact with the rotating pulley. There are five 
claims which embody the above subject-matter. Probably 
the primary object of the patent was to protect an invention 
important in laying telegraph cables, and from it the ergometer 
brake very naturally followed. 

Prof. W. E. Dalby informs me that Lord Kelvin told him 
that he invented the brake primarily in connection with the 
laying of the Atlantic cable for braking the cable as it was 
paid out. 

Flexible Band Dynamometer (by W. C. Unwin, from 
a paper read before Section G of the British Association, 
1883). 

The ordinary strap brake dynamometer, in which two 
weights are suspended from a strap which embraces a pulley, 
driven by the prime-mover to be tested, is described. If the 
suspended weights be called P and Q, of which Q is greater 
than P, then the work consumed in friction is expressed by 
V (Q_P) ? where v is the surface velocity of the pulley, or 
otherwise if 6 be the arc embraced by the belt, and /x equals 

Q 

the coefficient of friction, then p = e 1x9 , where e is the base of 

the hyperbolic logarithm, or for a given arc of contact Q = &P, 
k depending on the coefficient of friction. For the weights to 
remain at rest the coefficient of friction must be exactly 
constant. But since such a condition cannot be attained, 
oscillations are set up, which prevent very close readings. 
Such a condition has been modified in the Ayrton and Perry 
machine. If in place of one of the weights a spring balance be 


76 


DYNAMOMETERS 


employed, the dynamometer automatically adjusts itself to 
changes in the coefficient of friction. The author of the paper 
goes on to show how the friction of the pulley may be made 
still more independent of changes in the coefficient of friction. 

The method is as follows : Two pulleys, grooved for con¬ 
venience, are on the driven shaft, side by side. The band is 
attached to a spring balance placed below the pulleys ; it then 
embraces one of the pulleys, then passes downwards, and 
embraces one pulley and returns upwards to the second driven 
pulley, which it also embraces ; from its free end a weight is 
suspended. By means of this arrangement an alteration of 
20 per cent, in friction will alter the quantity Q — P less than 
6 per cent. Again, if the band be taken over four pulleys, 
then a variation of 20 per cent, in the frictional coefficient would 
alter the friction on the pulleys 1J per cent. By means of 
this four-pulley brake 3 feet in diameter running with a surface 
velocity of 50 feet per second a flexible wire band, carrying 
100 lbs. as the greater load, 8-8 horse-power could be absorbed. 
Since two or three wires might be used side by side, each carry¬ 
ing 100 lbs., large amounts of horse-power could be conveniently 
absorbed, the grooves and bands being cooled by jets of cold 
water. 


Application of the Rope Brake. 


THE ROPE BRAKE, USED IN TRIALS OF MOTORS AND ENGINES 
BY THE SOCIETY OF ARTS, 1888—89. 

These exhaustive tests of the output of different kinds of 
engines, including the 

Atkinson Gas Engine . . B.H.P. 



Crossley Gas Engine 


Duration of 


Griffin Gas Engine . . . ,, 12-51 ( run, 6 hours 

Paxman Portable Steam Engine. ,, 19-44 j 

were made by the late Prof. John Hopkinson, F.R.S., Mr. 
Beauchamp Tower, and Prof. Alexander Kennedy, F.R.S., 
who were appointed by the council of the Society of Arts as 
judges of the engine trials. The brake horse-power (B.H.P.) 
was in every case determined by means of a rope brake on the 
flywheel or on the flywheels of the engines under examination. 


FRICTION BRAKES 


77 


I have found a few engineers who speak disparagingly of the 
rope brake, but I have also found that their opinions were not 
based on personal experience of the brake ; they certainly 
would have been satisfied with it had they used it. In the 
hands of W. Thomson (afterwards Lord Kelvin) it was found to 
be a satisfactory brake, and a workable form of the brake was 
patented by him in 1858, as previously mentioned. In the 
engine trial I have cited, excellent results were obtained from 
its employment. In the report of the judges for the Society of 
Arts, 1880, we read, p. 5 :— 

“ The brake horse-power was in all cases ascertained by means of a 
rope brake upon the flywheel, or flywheels, of the engines. Two ropes 
were used for each wheel; they were kept at a proper distance apart 
and in fixed position upon the flywheel by means of transverse wooden 
distance pieces. The dead load was applied by means of weights, and 
the back tension necessary to put the friction on the brake by means of 
a spring balance. The spring balance was read every five minutes, and 
its tension was deducted from the dead load applied. This brake was 
found to work perfectly satisfactorily, and its results are certainly 
beyond suspicion. It is important, however, if any metal be used for 
attaching the wood cross-pieces to the ropes, that it shall not rub 
against the rim of the flywheel; if this should occur, the metal becomes 
exceedingly hot, and is liable to burn the rope.” 

The duration of an engine test in one case lasted 6*43 hours, 
the brake horse-power being 18*95, the weight on the lower end 
of the rope was 320 lbs., the spring balance reading 32 lbs.: so 
that the net brake load was 288 lbs. The flywheel in this 
case was of trough section, and water dripped into it and 
evaporated. No lubricant of any kind was employed on the 
surface of the brake. Manilla rope has usually been employed 
in this type of machine, and has given excellent results. 

In Fig. 33 a modification of the Thomson brake is shown. In 
place of the large weight acting by gravity, a Denison steelyard 
gravity balance was employed. The rope embraced the lower 
half of the pulley, a spring balance being attached to the other 
end of the rope. This form of brake was used in testing 
machines in the works of Messrs. Willans and Robinson. The 
figure is reproduced from an excellent paper in the Engineering 
Magazine of November, 1904, by Capt. H. Riall Sankey and 
Mr. C. Humphery Wingfield. I am indebted to the manager 


78 


DYNAMOMETERS 


of this magazine for his kind permission to reproduce the cut. 
In engine tests made by the authors of this paper the hydraulic 



Fig. 33. 


brake of W. Eroude was also employed and by its means good 
results were constantly obtained. 

Rope Brakes at the Central Technical College, London. 

Fig. 34 shows the brake of the experimental engine at the 
Central Technical College. I am indebted to Prof. W. C. 







FRLOTION BRAKES 


79 


Unwin, F.R.S., for the original drawing from which the figure 
was reduced. The brake wheel is of channel section (shown at 



the top right side), and when in operation is constantly cooled 
by water fed into the channel. The radius at which the load 
acts is fixed by a wooden block shown on the left of the figure. 












































80 


DYNAMOMETERS 


The spring balance is so placed that it can be readily adjusted 
by means of a screw and hand wheel. In another engine in 
the same institution, in which either of two wheels can be used 
as brake wheels, their respective diameters being 4 feet and 6 
feet, the dead weight of 140 lbs. and spring balance are used with 
a single Manilla hemp rope 1J inch in diameter. The rim of the 
flywheel is cooled, and the power absorbed is up to 7 or 8 horse¬ 
power. In another rope brake made to absorb 12 to 15 horse¬ 
power the load is 200 lbs., and two ropes are employed, their ends 
being fixed to blocks from one of which the dead weight hangs ; 
the other is connected to a spring balance by means of a single 
rope. The two ropes are kept in place on the face of the flywheel 
by three equi-distant blocks. In each case the effective radius 
at which the load acts is the distance between the perpendicular 
let fall through the centre of the flywheel and the parallel 
straight line through the centre of gravity of the load. No 
one watching these rope dynamometers when running can 
but be impressed by the simplicity of the device and its sur¬ 
prising steadiness for hours together. As long as the rope is 
dry the action is steady ; but not so when lubrication is intro¬ 
duced—the spring balance then oscillates to such a degree that 
readings cannot be readily made. 

A friction brake, formerly used at Cooper’s Hill College, is 
illustrated in Fig. 35, reproduced by the permission of the 
editor of Engineering. Several useful additions to the usual 
brake are shown, as devised by Mr. James Hopps of the 
Mechanical Laboratory, Cooper’s Hill College. The descrip¬ 
tion is slightly abridged from Engineering , April 17, 1903. 

The cooling water enters through the regulating cock A, 
passes through the flexible pipe B, and discharges into the 
channel of the rim of the wheel through C. The heated water 
is withdrawn through D. The pipes C, D, and D 2 are adjusted 
by means of the knurled knobs I and I connected to the worms 
and worm-wheels. The flow of both feed and discharge water 
can be accurately adjusted. By continuously depressing the 
collecting pipe D, the water can be quickly removed without 
flooding the engine-room floor. The best position and form 
of the supply pipe depends upon the velocity of the rotating 
wheel and the contained water; in the case before us the velocity 
of the innermost layer of water was 28 feet per second ; by 


FRICTION BRAKES 


81 


curving the pipe C to the same curvature as that of the rotating 
water and placing the jet at about 30 degrees from the bottom 
of the wheel the waters blend without splashing. 

The friction bands are applied on the top half of the wheel, 
and are loaded with a series of weights G, etc. The 50-lb. 



Fig. 35. 


capacity counter-spring at the other end of the band is not 
attached to the floor, but to a weight of 30 lbs., which rests at 
the bottom of the tube H. 

Should the engine suddenly slacken speed the weights G 
will descend about 2\ inches, when they will come to rest, and 
the counter-spring will raise the 30-lb. weight through a corre- 










82 


DYNAMOMETERS 


sponding distance in the tube H. This prevents any over¬ 
straining of the counter-spring. Any danger that might arise 
from the weights G overrunning is prevented by a tail-pin with 
collar passing through the bottom of the tray. 

The brake dynamometers of Thomson, Imray, Carpentier, 
Reckenzaun, and Raffard form a small class of machines, in 
which by different constructions the same principle of auto¬ 
matic government of friction is employed. In order to keep 
W 

e (which equals —) constant 6 is made to vary inversely 


as /x. 

The Dynamometer of James Thomson. 


On the shaft driven bv an engine, or on the shaft of the 


engine itself, two pulleys of 



equal diameter are carried, one 
keyed to the shaft and the 
other loose on it (Fig. 36). The 
fast pulley is the brake wheel, 
while the function of the loose 
pulley is to carry a portion of 
the brake band or strap, which 
partly embraces both of the 
pulleys. The weights W and 
w are adjusted so as to balance 
the torque (a word invented 
by the late Professor James 
Thomson). Should, however, 
/a increase, then the loose pul¬ 
ley is rotated a little, and its 
movement lessens the angle 6 
embraced by the band on A 
and thus automatically keeps 
e* 9 constant. 

The Dynamometer of J. 

Imray (Figs. 37 and 38). 


The automatic adjustment 
in this dynamometer is obtained by altering the arc of 
contact of the rubbing surface. The brake pulley A is partly 
embraced by a succession of wood blocks attached to a 




















FRICTION BRAKES 


83 


flexible brake strap EGF. This is fixed to a counterpoised 
sector-shaped frame ECDD moving about a line in the axis 
of the shaft B, the radius of its arc being equal to that of 
the brake strap, one end of which hangs vertically and is 
loaded with a weight W; the other end also hangs vertically 
and is loaded with a less weight P. If the weights be adjusted 
so that the brake absorbs the power required and ju. changes 
(decreases, for example), then the load falls a little, and in doing 



Fig. 37. 


so causes the brake strap to bring a larger surface of brake 
block in contact with the pulley, thus restoring equilibrium 
until the next disturbance takes place. The genesis of the 
dynamometer of Imray is so good an example of mechanical 
evolution that I have quoted in full a passage which occurs 
in the discussion which followed a paper by Mr. W. W. Beau¬ 
mont, Institution of Civil Engineers, Vol. XCV., 1888—89, 
Part I., p. 57, due to Mr. Imray, who said :— 

“ It was many years since the late Mr. William Froude and lie 
investigated, at considerable length, the conditions of the frictional 

G 2 

































84 


DYNAMOMETERS 


hold of belts upon pulleys, and the result was communicated in a 
paper by Mr. Froude to the Institution of Mechanical Engineers (Proc., 
1858, p. 92). The first thing they had to look at was this. At that 
time amongst engineers there was a fallacy prevalent that the larger 
the pulley the greater was the frictional hold of the strap upon it. They 
disposed of that by trying pulleys of all sizes from 5 inches to 5 feet, with 
straps on them loaded with weights, and there was not a shadow of 
difference between them. The diameter of the pulley had nothing to 
do with the frictional hold. They then investigated the question, and 
they thought that they were the first who had come to the formula for 
frictional hold, which was very much like the one given by Prof. Ayrton. 



ScaUftp 0 ’ '"'•' f ■■■..?.f _ i _5_ i _ ti Fe ^ 

Fig. 38. 


It appeared from that formula that a change in the number of degrees 
of the arc of contact made a great change in the frictional hold. For 
instance, they found that if one weight was 1 lb. and the other weight 
was 3 lbs., when half the circumference was embraced, then the latter 
would be 9 lbs. when the whole circumference was embraced, when three 
halves 27 lbs., and so on according to the formula. It therefore appeared 
to him that the best way of making a brake automatically adjustable 
was to make it alter for itself the amount of circumference embraced 
by the strap. For that reason he schemed the brake shown in Figs. 37 
and 38. There were two arms, one on each side of the wheel. Those 
arms carried metal straps, by which the large weight was hung ; and to 
the top of those arms at F the brake strap was attached. Whenever the 
weight rose it took a less part of the circumference ; when it descended 


















































































FRICTION BRAKES 


85 


it took a greater part of the circumference, so that it always cured itself, 
and it kept very steady. He believed that Mr. Froude used it, and to a 
large extent had found it successful.” 

The Dynamometer of Carpentier (Bulletin Societe des 
Anciens Eleves des Ecoles Nat. des Arts et Metiers, No. 186, 
1880). 

In this machine the automatic adjustment is obtained by 
utilising the same principle, but instead of a band a rope is 
employed, which is held at its mid-point by a hole in a flange 
projecting from the loose wheel. The rope is coiled twice 
round the pulley keyed to the shaft, and twice round the 
loose pulley. This dynamometer proved itself useful in 
finding the power delivered by small dynamos. Carpentier’s 
dynamometer was remodelled and improved by I. Raffard, 
so that larger powers could be dealt with, such as 6 h.p. 
(Bulletin of the society quoted above, No. 212). In this 
machine three equal pulleys are carried on a shaft close 
together. The middle one is fast on the shaft and the two 
external pulleys are loose on it. A balanced bar shaped like 
an E, but without the small middle projection of this letter, 
is free to rock about its ends, which are centred on the axis of 
the shaft, on either side of the three pulleys. Three steel 
bands are attached to that part of the bar which faces the 
pulleys. The central band passes over the fast pulley in a 
contrary-to-clock-hands sense, and is loaded with a weight P. 
The two other bands are carried under the two outer pulleys 
in a clock-hands sense, and are attached to the end of a scale 
beam, so that they are loaded by means of weights suspended 
from the other end of the beam. When the central pulley is 
driven by the motor under trial, contrary-to-clock-hands, the 
arc embraced by the outer bands varies inversely as the friction 
of the central band. Thus compensation for change of friction 
is established, as in the brakes of Imray and Carpentier. The 
pulleys and the bands were partly immersed in a water trough. 
This dynamometer was improved by A. Reckenzaun, so that 
larger powers could be dealt with. 

[Another way of making the effective friction of the belt 
of a brake change according to its position is described in the 


86 


DYNAMOMETERS 


Electrical World of New York, March 9, 1907, p. 520. This is 
attributed to Scheibe. An ordinary leather belt hangs over 
the brake pulley, with a light weight on the side in contact 
with the downward moving side of the pulley and a heavier 
weight on the other side. The difference of the two weights 
multiplied by the effective diameter is the torque. One half 
of the belt at the end carrying the greater weight is studded 
with copper rivets with their flat heads on the side next the 
pulley. The friction of these is so much less than that of the 
plain leather that the belt automatically takes its place where 
the balance is exact. An example is given showing a ratio of 
change of 1 to 10. Only small weights are contemplated.] 

The Friction Dynamometer of Prony. 

To Prony must be attributed the earliest method of testing 
the output of a prime-mover by means of a brake acting on a 
driven pulley. The Prony brake in its simplest form con¬ 
sisted of a pair of brake blocks partly embracing a pulley. 
From one of the blocks an arm projected which was loaded 
with a weight. In Fig. 39 a diagrammatic sketch is shown 
of the brake. The required pressure on the pulley was 
obtained by regulating the nuts above the lever arm. Let us 
suppose that a weight of 100 lbs. was suspended from the arm, 
and that its line of action measured horizontally was 6 feet 
from the axis, also that the pulley made 300 revolutions per 
minute ; if there were no sliding of the brake over the pulley 
the weight would be drawn up just as if the rope were coiled on 
a pulley of 6 foot radius, so that the work is equivalent to 
100 lbs. raised at the rate of 277 x 6 X 300 feet per minute, 
and the brake horse-power is equal to 
2 tt X 6 X 300 X 100 

33,000 “ 6 6 ' 

I am indebted to the manager of the Engineering Magazine , 
November, 1904, for the figure shown. In this ideal case the 
rope is supposed to have no thickness. For practical purposes 
this brake is usually made with a brake block on the under 
side of the pulley, and a row of small blocks attached to a 
flexible band embracing the upper half-circumference of the 
pulley ; also the weight is suspended from an arc-shaped limb 



FRICTION BRAKES 


87 


which forms a part of the lever arm. This prevents the value 
of the load changing when the arm is deflected on either side of 
the horizontal position. The whole is counterpoised with a 
weight which can he adjusted. The capacity of this form of 
dynamometer for measuring power has been assumed to lie 
between 5 and 200 horse-power. Thurston designed a water- 
cooled brake dynamometer of the Prony type to absorb 



540 horse-power. The brake wheel was 5 feet in diameter, 

2 feet over the face, and ran at 100 revolutions per minute. 
It was embraced by two brake straps lined with wood blocks 

3 inches wide. The brake wheel was well lubricated with 
lard and plumbago. Something under 200 horse-power 
appears to have been absorbed by this dynamometer (Journal 
of the Franklin Institution, Vol. XCI., p. 290). The indica¬ 
tions are good when the output of the engine or motor is fairly 
constant, but with varying powers the inertia of the arm 

























88 


DYNAMOMETERS 


interferes with steady running and renders the indications 
difficult to estimate. An exhaustive note on the oscillations 
set up in this form of brake dynamometer will be found in the 
Proceedings of the Institution of Civil Engineers, Vol. XCV., 
pp. 41—47, by R. E. Eroude. When instead of a brake block 
system a rope is employed to produce the required friction, a 
mass having a considerable moment of inertia is avoided as is its 
consequent oscillation and steady readings are easily obtained. 

The Brake Dynamometer of Mr. Coope (Proceedings of 
the Institution of Civil Engineers, Vol. XCV., p. 49). 

In this machine the pulley is almost entirely embraced by 
wood brake blocks, attached to a flexible brake strap which 
was divided into two parts, each covering about one-third of 
the face of the pulley, and leaving an intermediate space 
between them which was filled by four cords, which partly 
embraced the pulley. Regarding the pulley as the face of a 
watch, the cords were attached to the brake straps at X, 
and were a tangent to the pulley at III. The greater of two 
weights was suspended from a cross bar connecting the two 
brake straps, and was raised when the pulley revolved in the 
clock-hands sense. The friction of the brake straps was 
regulated by a screw which connected its ends together. A 
smaller weight was suspended from the cords (four side by side) 
hanging from the other side of the pulley. If by any increase 
of friction the greater of the two weights was raised, the arc 
embraced by the cords was reduced, and consequently the 
friction. If the friction decreased, then more arc was covered 
by the cords, so that good compensation was the result. It was 
suggested that complete balancing would have been effected 
by hanging a group of the same sort of cords from the bottom 
of the two weights after the manner of a festoon. 

I may notice that this would not be the case unless the 
hanging ropes were of infinite length. A rope of finite length 
hanging from two weights would approximately form a cate¬ 
nary curve, and the two weights would be drawn together and 
consequently their pulls would not be in vertical lines. If the 
hanging ropes passed round a pulley (in a block) of exactly the 
same diameter as the brake pulley, then balancing would 


friction brakes 


89 


exist. In this machine the method of compensation is some¬ 
what similar to that employed by James Thomson. The 
details, however, differ materially from those of Thomson’s 
machine. 

The Friction Brake of Appold and Amos. 

This brake was primarily designed for controlling the rate of 
pay-out of the French Atlantic cable before the year 1858. 
The pulley to be controlled was embraced by a brake band, 
and its ends were attached to two points in the lever shown in 
Fig. 40. At the end of the lever was a short slot A engaging 
with a fixed stud ; if the friction between the band and the 
pulley increased, the lever was moved 
to the left, and the brake band 
slightly released thereby and the 
friction reduced. The brake main¬ 
tained a uniform tension on the 
cable while it was being paid out. 

This brake when employed as a dyna¬ 
mometer by the Royal Agricultural 
Society for testing engines was some¬ 
what modified. The driven pulley 
was embraced by a flexible band lined 
with numerous wood brake blocks. 

The toggle lever was placed at the lowest part of the circum¬ 
ference of the pulley, a weight was suspended from a hook pro¬ 
jecting from the brake band in line with a horizontal diameter, 
and by means of a regulating screw the required friction was set 
up. The correct working position of brake band was indicated 
by a pointer and the readings taken when in this position. The 
brake used for paying out purposes appears to be excellent, but 
considerable doubt has been felt as to its correct performance 
as a dynamometer. The toggle lever introduces conditions 
which if not entirely accounted for might cause error. The 
brake is certainly interesting from a historical point of view. 
Experience has shown that the utmost simplicity must be aimed 
at in connection with the automatic regulation of the friction 
brought into play. 










90 


DYNAMOMETERS 


The Brake Dynamometer of Balk. 


In this machine a compensating lever is employed, connected 
to a flexible band lined with wood brake blocks, as in the Appold 
brake, but in this dynamometer the lever is situated outside 
the circle of the pulley, and its external end is made with a 
slot which is large enough to allow of some play between it and 
a fixed pin. To the end of the lever, in line with the pin, a 
scale pan is suspended. From the face of the brake strap most 
distant from the lever a weight hangs ; rotation contrary-to - 
clock-hands tends to lift this weight. The initial tension of 
the brake strap is regulated by means of a left and right hand 
screw which connects its ends. When the machine is working 
the load in the scale-pan is adjusted so as to keep the lever 
floating, and not touching the pin which passes through the 
slot. The effective moment equals P r 1 -pr 2 and the horse¬ 
power absorbed equals — ^33 ooo^ ^ ' 


The blocks which lined 


the brake strap were made of beech or plane-tree wood. The 
pulley and blocks were well greased, and it was found that 
with but little attention a run might be made for a whole day. 
The dimensions of one of these brakes, used by Messrs. Ran- 
somes, Sims, and Jefferies, were as follows :—Diameter of brake 
wheel, 6 feet ; width, 1 foot, load suspended from flat steel 
spring tapes at a radial distance of 3-183 feet. By means of 
a lever at the side of the pulley a counter could be thrown 
into gear. 


A Water-cooled Brake Dynamometer (by Messrs. R. 

Garret and Sons). 

In this machine a brake strap lined with beech-wood blocks 
embraced the driven wheel. The strap was compensated for 
friction by the Appold lever, and the loading and method of 
tightening are the same as in that brake ; but an important 
improvement was introduced, namely, a water channel in the 
rim of the brake wheel. Water was introduced by means of a 
tube which dipped into the channel, which it left by evaporating. 
The rim of the wheel was thus kept cool and also the brake 
blocks. 



FRICTION BRAKES 


91 


[The Griffin Engineering Company’s Brake.] 

[ A neat and portable absorption dynamometer constructed 
by the Griffin Engineering Co., Ltd., of Bath, is described and 
illustrated in Engineering , February, 1912,-p. 572, and also in 
Internal Combustion Engineering , January 7, 1914. Lignum 
vitae shoes may be pressed against the interior conical faces of 



Fig. 41. 


the friction drum by means of a stationary hand-wheel through 
the intervention of mechanism the nature of which is made 
sufficiently clear in the illustrations (Figs. 41 and 42), for which 
I am indebted to the makers. Water is passed through the 
interior to keep it cool. The direction of rotation is such that 
the long arm, which is stayed as shown, tends to lift the weight 
at its end. The force there exerted is measured by the aid of a 
spring balance, and as usual the horse-power is known when 
the speed of rotation, the length of the arm, and the force at 







92 


DYNAMOMETERS 


its end are known. A socket is provided on the opposite side 
of the casing to take the arm when it is desired to test the horse¬ 
power of a shaft running in the opposite direction. This 
appears to the writer to be a particularly neat and convenient 
form of dynamometer, and though included among the friction 
brakes it might equally well have been described in the next 
chapter among fluid friction brakes, for it is only when being 
used at its highest power or at low speeds that solid friction is 
made use of. For ordinary use at high speeds the shoes are 
removed out of contact with the friction surfaces by means of 

the hand - wheel, and 
“water attrition” alone 
is relied upon for taking 
up the load. It is on 
this account that this 
dynamometer is espe¬ 
cially suitable for testing 
petrol motors, for the 
higher index law of fluid 
friction, as explained on 
page 226, is necessary to 
obtain stability of speed 
with this type of motor. 
The makers recommend 
that water should be 
supplied at the rate of 
about five gallons per 
brake horse-power hour. 
The inlet and outlet water pipes are shown at the bottom of the 
casing. The distance between the shoes and the casing or the 
pressure between them may be regulated by the hand-wheel and 
the resistance adjusted while the load is on. This dynamometer 
is convenient in that the water supply may be taken from a 
tank very little above the dynamometer level, as no hydrostatic 
pressure is required to overcome internal pressures. According 
to tests made in the presence of the representative of the 
journal, Internal Combustion Engineering , on a dynameter made 
for the Hong-Kong University, the indications of this dynamo¬ 
meter are unusually steady as compared with those of an 
ordinary friction brake. Four sizes are at present made. 



Fig. 42. 






















FRICTION BRAKES 


93 


No. 3, with discs 21 inches in diameter, is suitable for powers 
ranging from 5 horse-power at 250 revolutions per minute to 
70 or 80 horse-power at 3,000 revolutions per minute.] 

[Alden Absorption Dynamometer.] 

[There is an account of a very large Alden absorption dynamo¬ 
meter in the Electrical World (New York) of October 31, 1908, 
p. 945 ; see also Trans. Amer. Soc. Engineers, Vol. XI. A 
central cast-iron plate keyed to the shaft runs in a casing which 
is free and the torque of which is measured. Copper plates 
attached to the casing lie one on either side of the cast-iron 
plate. Water is fed into the casing at any desired pressure and 
circulated, and according to the pressure so the friction between 
the copper and the iron may be varied. Oil is circulated 
between the friction surfaces. The power that can be absorbed 
is limited by the heat which can pass through the copper plates. 
“ Since the maximum peripheral speed should not exceed 
7,000 feet per minute and the best friction surface is between 
6 and 10 square inches per horse-power, the large capacity 
brakes require more than one disc.” The figure shows a 
60 inch four-disc brake in the bearings of a pulp grinder and 
directly connected to the water wheel. It absorbs 3,000 horse 
power when operating at a speed of 225 revolutions per minute. 
The dynamometer is given an automatic control, depending 
on the regulation of the water pressure, by the slight move¬ 
ments of the casing.] 

[Nicholson’s Lathe Tool Dynamometer.] 

[In the Proceedings of the Institution of Mechanical Engi¬ 
neers, June, 1904, pp. 883—925, there is an interesting and. 
important paper by Prof. J. T. Nicholson, of the Municipal 
School of Technology, Manchester, entitled “ Experiments with 
a Lathe Tool Dynamometer.” Reference is made to the few 
previous investigations on the same subject. Hastig published 
a work in Leipzig in 1873. Mr. A. Mallock published in the 
Proceedings of the Royal Society, December, 1881, a paper on 
experiments which he had made in the engineering workshop 
at Cambridge. Prof. R. H. Smith, in his work on Cutting Tools 


94 


DYNAMOMETERS 


published in 1882, gave the results of experiments which he 
had made. 

In the second and more complete lathe tool dynamometer of 
Prof. Nicholson the tool is supported so that it can move about 
both a vertical and a horizontal axis at the back end, being 
supported immediately under its cutting end by means of a 
powerful lever or resting upon a knife edge in the middle,' 
while the vertical force due to the cut is transmitted by the 
strut which supports the cutting end of the tool and which 
rests upon a knife edge at one end of the lever. The up 
thrust at the other end of the lever, which is at the back of the 
lathe, is similarly transmitted by a knife edge and strut to a 
diaphragm gauge filled with boiled distilled water. The water 
communicates by a pipe with a Bourdon pressure-gauge. By 
this means the vertical force on the tool can be ascertained, 
and at the same time the movement, even with forces as great 
as 15 tons, is excessively small. A corresponding device 
measured the traversing force needed to make the tool follow 
the feed, and a third measured the radial force necessary to 
keep the tool up to its work. Experiments were made with 
tools of various shapes taking off shavings of mild steel or 
cast iron of different thicknesses and breadths and at different 
speeds. The power required to cut mild steel or cast iron is 
the same and is just over 2 horse-power per pound per minute, 
while provision must be made for a vertical force of about 
100 tons per square inch of section of shaving. In addition 
to this much information of importance as to the tools and 
their durability and the power required with different cutting 
angles and also as to the forces which must be met in the 
design of the lathe was obtained. Other experiments with 
the same object were referred to in the discussion. As there is 
no provision in the scheme of the book for this I have put 
this among the absorption dynamometers, for strictly speaking 
it is one.] 


CHAPTER V 


WATER BRAKES 

Historical . . . 

Hirn . 

Perry liquid friction 
Reynolds 
Froude 

Heenan & Froude . 

Brotherhood. 

Historical. —G. A. Hirn,* while working on the mechanical 
equivalent of heat, devised a method of finding the heat pro¬ 
duced by the friction of water, in which he employed con¬ 
centric tubes ; the inner one rotated, while the outer concentric 
one was free to rotate, but in doing so raised known weights. 
This appears to be the prototype of hydraulic dynamometers, 
in which some rotating internal organ imparts motion to an 
outer casing through a liquid connecting medium. The work 
of Hirn is of such importance and interest that I give here a 
translation of his description of the apparatus. 

“ Friction of Water .—In studying this I have employed apparatus 
constructed thus. Firstly, a polished brass cylinder 30 centimetres 
diameter and 100 centimetres long, mounted on an axis connected to a 
motor having a very regular rate of rotation, and capable of a variation 
of speed between 60 and 600 revolutions per minute. Secondly, a fixed 
(external) cylinder, polished inside, placed concentric with the former 
internal one and distant from it by 3 centimetres. Discs furnished 
with stuffing-boxes, through which the axis of the internal cylinder 
passed, formed the ends of this external cylinder. The whole space 
between the two cylinders could be filled with any liquid, which was 
prevented from leaking out by the stuffing-boxes. 

“ When the internal cylinder rotated in either direction, the friction 

* “ Theorie Mecaniqu§ de la Chaleur,” 2nd ed., 1865, p. 65, and 3rd ed„ 1875, 
p. 92. 


. 95 

96 
. 98 

. 98 

. 108 
. Ill 











96 


DYNAMOMETERS 


which its external surface exerted upon the water, and which the water 
in turn exerted on the internal surface of the external cylinder, tended 
to rotate it about itself. Two parallel levers fixed to its two ends 
carrying balance pans allowed the rotation to be checked by loads 
which showed the value of the friction. The ‘ tare ’ of the levers and 
the value of the friction due to the stuffing-boxes were easily found by 
making the internal cylinder rotate very slowly in opposite directions. 
By means of two vertical pipes fixed as close as possible to the stuffing- 
boxes a continuous current of water under perfect control could be 
passed through the apparatus. The temperature of the liquid was 
taken as it entered and also as it left the apparatus. As far as possible 
the temperature of the water entering the apparatus was kept as many 
degrees below the temperature of the room as the water leaving the 
apparatus was above it. The law of cooling of the apparatus was 
carefully determined, so that it was easy to make the necessary correc¬ 
tions, which were always small. This apparatus, as a whole, con¬ 
stituted a veritable liquid friction balance. It enabled one to learn the 
work expended on this or that liquid for any speed, and also the calories 
produced by this friction, in a liquid whose specific heat was known. 

“ Owing to the large size of the apparatus and the speed which the 
internal drum received, this apparatus allowed of a considerable amount 
of mechanical work being employed—750 kilogram-metres per second, 
or 10 horse-power (French measure).* I insist on the importance of 
this feature, as a guarantee of the exactitude of the numbers found. 
The results deduced have been satisfactorily regular. Six experiments 
using water and various speeds, and different amounts of liquid intro¬ 
duced per second between the two drums, have given me 432 kilogram- 
metres as the work which produced one calorie, and hence the value of 
the heat equivalent. The water friction experiment took its origin 
from Joule, and after him Favre. The values obtained by these two 
experimentalists differ a little from those I have given (Joule found it 
to be 424 kilogram-metres).” 

Recent determinations make the value 428. 

There is an interesting experimental method of finding the 
friction between a liquid and a solid, which may be considered 
in this connection. It is due to Prof. J. Perry, F.R.S. I 
give here a sketch of the method, which is described more fully 
at pp. 76—78 of his “ Applied Mechanics,” 1897. It has to do 
with the resistance to motion of water in a pipe or the resist- 

* 75 kilogram-metres per second = force de chevah The horse-power English. 
= 1 01386 force de cheval. 


WATER BRAKES 


97 


ance to tlie steady motion of a ship. Usually the motion 
between a liquid and a solid is complicated. The simplest 
motion is in parallel layers. We may imagine two infinite 
parallel boundaries with the fluid between them, one at rest 
and the other moving with a uniform V, and that the fluid 
adheres to each boundary. Let the distance between the two 
adjacent surfaces be b, then the tangential force per unit area 


required to keep up motion is 


i*V 


is the coefficient of vis¬ 


cosity. Theoretically jjl should be constant, if the motion is in 
truly plane layers. Since an experiment with infinite surfaces 
is impossible, the condition required was approached by 
employing the apparatus shown 
in the figure (Fig. 43). FF is 
a hollow cylinder so supported 
that it cannot move sideways. 

Resistance to rotation is op¬ 
posed by a torsion wire A, by 
means of which it is suspended. 

This cylinder dips into an 
annular space between two 
surfaces filled with liquid and 
wetting all the surfaces. When 
the vessel EDDE is rotated 
about its axis the liquid moving 
past the cylinder F tends 
to rotate it. The torsion wire A resists this torque due 
to friction, and the value of the twist of the wire shown 
on a scale becomes a measure of the viscosity of any liquids 
which may be experimented on. The apparatus of Pro¬ 
fessor Perry was designed and partly constructed in Japan 
in 1876. An important paper by him will be found in 
the Proceedings of the Physical Society, London, Vol. XII., 
pp. 236—255. The following facts were ascertained. At 
constant temperature, below a certain critical speed, experi¬ 
ment showed that friction was proportional to velocity ; so 
that [A could be found. The law changed at the critical 
speed, and above it friction was seen to be proportional 
to a higher power of the speed than unity, /x was found 
to decrease rapidly with increase of temperature. For inf or- 



Fig. 43. 























98 


DYNAMOMETERS 


mation on critical speed, see Philosophical Transactions of 
the Royal Society, Part III., 1883, Osborne Reynolds, 
F.R.S. It would be foreign to my subject to give exhaus¬ 
tive references to researches on friction due to fluids in 
motion. I have introduced this interesting experiment, 
since by its means the properties of the kind of friction 
generated in the apparatus of the type of that employed by 
Hirn were determined. 

In 1876 0. Reynolds, while experimenting on a multiple 
steam turbine at speeds of 12,000 revolutions per minute, 
employed a water brake, or, in his words, “ having a centri¬ 
fugal pump suspended on the shaft and working into itself,” 
the head against which the centrifugal pump was working 
being regulated by a valve situated in the external circuit of 
the water. An account of this apparatus was given before the 
Mechanical Section of the British Association in 1887. It was 
at this meeting that the paper on the water brake of William 
Eroude was also given. In both machines the resistance to 
turning was regulated by adjustable sluices arranged to cut off 
the passage of the liquid within the casing. Reynolds remarks 
that “ Mr. Froude invented an internal arrangement which 
affords a resistance out of all comparison with any other form.” 

For the exact details of 0. Reynolds’ hydraulic dynamo¬ 
meter “ Scientific Papers of O. Reynolds, F.R.S.,” Vol. II., 
pp. 353—359, should be consulted. I give a rather detailed 
account of the remarkable water brake of William Froude, and 
a description of the modern form of the brake designed and 
made by Messrs. Heenan and Froude, which has been success¬ 
fully employed in testing engines of considerable horse-power, 
in some cases reaching 2,000 B.H.P. 

The Turbine Dynamometer of Froude. 

In July, 1877, a very remarkable paper was read before the 
Institution of Mechanical Engineers at their meeting at Bristol, 
the title of the paper being “On a new Dynamometer for 
Measuring the Power delivered to the Screws of Large Ships,” 
by Mr. William Froude, F.R.S. The original paper should be 
carefully read to appreciate the genius of William Froude. In 
hydrodynamics it stands out as a monument to mathematical 


WATER BRAKES 


99 


acumen and its practical application. The following abstract 
will perhaps be of use to those who are unable to obtain the 
original paper.* 

For the measurement of fairly small powers the friction - 
brake dynamometer is effective and simple, but serious diffi¬ 
culties arise when the horse-power to be absorbed is great and 
of the order of thousands instead of tens of horse-power. In 
the case of a friction-brake work-measuring machine the engine 
in delivering its power will be virtually winding up a weight 
out of a well of indefinite depth ; but the weight, instead of 
being constant, will vary with the speed of rotation, just as 
the resistance of a propeller does ; and so the work done by 
the engine tested will more closely resemble its natural work, 
and the same circumstance renders necessary some method of 
recording the changes of resistance occurring during the trial. 
Instead of the continuous friction due to two surfaces in con¬ 
tact, it will be seen that the total reaction will be due to the 
impact of fluid streams maintained in a state of intensified 
speed by means of a sort of turbine rotating within a casing 
full of water ; the turbine and the casing are mounted on the 
screw shaft in place of the screw, and while the turbine rotates 
the casing is held stationary by means of a lever pressing 
against a spring. 

“ The jets are alternately dashed forward from projections in the 
turbine against counter-projections in the interior of the casing, tending 
to impress forward rotation upon the casing, and are in turn dashed 
back from the projections in the casing against those of the turbine, 
tending to resist the turbine’s rotation. The important point is, that 
the speed of the jets is intensified by the reactions to which they are 
thus alternately subjected; and thus in virtue of this circumstance a 
total reaction of very great magnitude is maintained within a casing of 
comparatively very limited dimensions.” 

The construction of the apparatus is shown in Figs. 44—51. 
In Fig. 47, A is the screw end of the screw-shaft, BB the section 
of “ the turbine,” which consists of a disc with a central boss, 
keyed to the screw-shaft. The disc is shaped into a channel of 
semioval section extending round the whole circumference. A 

* I am indebted to the Institution of Mechanical Engineers for their kind per¬ 
mission to reproduce parts and figures from the paper mentioned. 

H 2 


100 


DYNAMOMETEKS 

































former representing the front, the latter the back ; its face is 
also shaped into a channel, a counterpart of that of the turbine 

























































102 


DYNAMOMETERS 


disc. The semioval channels nearly touch, and in effect form 
one complete oval channel, though the halves are separated 
by an imaginary plane of division. The boss of the casing is 
an easy fit over that of the turbine ; thus the turbine carried 
by the shaft can revolve within the casing without touching 
it, while the casing itself is stationary ; and one half of the oval 
channel is rotating while the other half is at rest. The two 
half-channels are not unobstructed, but they are each cut 
across by a series of diaphragms, as shown in Fig. 49, in which 
a single diaphragm is drawn. The diaphragms are semicircular 
in outline, so that when set obliquely their circular edges are in 
contact with the bottom of the channel and their diameters 
span the major axis of the oval. 

One of the diaphragms is shown in Fig. 50 end on. Each 
half-channel has twelve of these diaphragms, dividing it into 
a series of cells, two half-cells together making one complete 
cell with circular outline. The oval channel may be regarded 
as a series of obliquely placed circular cells. 

“ As the function of the turbine is to rotate while the casing remains 
at rest, one half of each cell is moving past the other half in such a 
manner that the moving half, if viewed from its stationary counterpart, 
would by reason of the oblique direction of the diaphragms which form 
the cell sides appear to be advancing antagonistically towards it; 
indeed, the motion virtually constitutes such an advance, because the 
bottom of each moving half-cell is continuously growing nearer to the 
bottom of the stationary half-cell which it faces. 

“ The effectiveness of this combination to resist rotation will be seen 
to depend essentially on the gwasi-antagonistic virtual approach of the 
moving to the stationary half-cells. The channel and casing is filled 
with water. When the turbine rotates, the water in each of its half-cells 
is urged outwards by centrifugal force; and subject to this impulse it 
forces inwards the water in the half-cells of the stationary casing, and 
so a continuous current is established—outwards in the half-cells of the 
turbine, inwards in the cells of the casing. 

“ The current originated by centrifugal force only, when once started 
possesses a power of growth independent of centrifugal force, but depen¬ 
dent on what has been called the virtually antagonistic motion of the 
two sets of diaphragms, and the cells of which they are the boundaries. 
The nature of this power of current-growth is discussed in an appendix. 
It was found that, with any given speed of the turbine, the system of 
internal motions gives rise to a speed-producing power called ‘ potential,’ 


WATER BRAKES 


103 


which will continuously increase the speed of the currents up to the 
point at which the friction experienced by them when traversing the 
cells produces a resistance which equals the potential. The frictional 
resistance and also the potential are both proportional to the speed of 
the turbine, so that the speed of current is directly proportional to the 
speed of the turbine simply. It is not difficult to trace the manner in 
which the established currents produce the dynamometric reaction. 
The result is not affected by the slight departure from truly cylindrical 
form of the cells. Each of the circular discs of water will constitute a 
sort of vortex. The mode in which reaction takes place is clearly 
described thus.” 

Now each vortex in virtue of the centrifugal force, which is 
continually tending to stretch it edgeways, pushes against its 
circumferential boundaries ; and as these boundaries are in 
fact made up of the bottoms or circular outlines of the two 
half-cells occupied by the vortex (the one in the stationary 
casing and the other in the rotating turbine), the resultant 
force, measured in the plane of rotation of the turbine, is 
constantly tending with a determinate force to stop the 
rotation of the turbine and create rotation in the casing. 

The magnitude this force may be expressed as due to the 
reversal of the sum of the momenta of the vortex streams, 
measured in the plane of rotation of the turbine ; since streams 
when entering a cell are flowing in one direction, and in the 
opposite direction with the same velocity when leaving it, and 
the force due to this reversal is directly proportional to the 
momentum reversed per second, this equals the product of the 
mass acted on per second and the change of speed imparted to 
it in the plane of rotation of the turbine ; also the mass acted 
on per second varies as the mean speed of the vortex current, 
and this depends on the speed of the turbine : thus the tendency 
of the vortex to resist the rotation of the turbine and to rotate 
the casing is as the square of the speed of the turbine. Even if 
the turbine were suddenly stopped, the “ vortical rotation 
would continue until extinguished by friction. 

There is yet another element of reaction existing only when 
the turbine is rotating. It is due to the fact that the hoop- 
shaped streams of the vortex stream is constantly sheared by 
the passage of the planes of the diaphragms of the turbine and 
also of the casing. The effective stream-speed is not changed 


104 


DYNAMOMETERS 


by this, since owing to the incompressibility of water each 
imaginary pipe must everywhere be traversed at the same 
speed ; but, from the action, the particles which form each 
stream at the points of shearing must be subjected to alternate 
changes of speed in the plane of rotation of the turbine. In 
passing from the stationary casing to the turbine cells, they 
assume the speed of the turbine in its plane of rotation and thus 
react on the diaphragms of the turbine with a definite force, 
proportional to the amount of momentum per second imparted 
to them as they pass. Again, in passing from the turbine cells 
to the cells of the casing, they lose that speed in the plane of 
rotation of the turbine, and so act on the cells of the casing, 
tending to push them forward with a force equal to that 
reaction which tended to stop the rotation of the turbine cells, 
the same mass being acted on each second in each instance* 
and as the same speed is in one case added and in the 
other deducted, the force is the same. Again we see that 
the reaction varies as the square of the speed of rotation 
of the turbine, since the momentum generated per second, 
causing the reaction, varies as the product of the mass 
operated on per second and the speed imparted to it ; the 
speed is that of the turbine, and the mass operated on varies 
as the speed of “ vortical rotation,” which is as the speed of 
the turbine. 

The conclusion arrived at from the theory of the turbine 
dynamometer by Froude was that “ their respective moments 
of reaction, with the same speed of rotation in each, should be 
as the fifth powers of their respective dimensions.” Experi¬ 
ment showed that this deduction was true. Two similar water 
dynamometers were made, in which the diameters of the 

12 \5 


turbines were 12 and 9-1 inches and 


(rj 


= 4, so that at a 


given speed of rotation of the turbines the ratio of the moments 
of the two machines should be 4. The ratio turned out to be 
3*86. The small difference is attributed to the fact that in the 
larger of the machines the internal friction was rather less in 
proportion than that in the smaller one. 

The analysis and the final deduction enable the engineer to 
design a turbine dynamometer to deal with horse-power of large 
value. The dynamical principles of the machine are clearly 


WATER BRAKES 


105 


set forth on pp. 252—260 of the Proceedings of the Institution 
of Mechanical Engineers, July, 1877. I have introduced this 
perhaps rather intricate description of the Froude turbine 
dynamometer, as at the present time (1910) a dynamometer 
designed on the Froude principle by Messrs. Heenan and Froude 
has been employed to “ brake,” a steam engine of 1,500 brake 
horse-power, built by Messrs. Browett Lindley & Co. The 
dynamometer was capable of absorbing 2,000 brake horse¬ 
power at 250 revolutions per minute. 

The paper by Froude terminates with an illustration of 
the way in which the acceleration of the water stream is pro¬ 
duced, and also by an illustration of the same principle by 
the late Sir Frederick Bramwell. The statement that “ for 
two strictly similar but differently dimensioned instruments, 
the respective ‘ moments of reaction ’ with the same speed of 
rotation in each would be as the fifth power of their respective 
dimensions ” is arrived at thus 

Let two dynamometers, A and B, be compared, the diameter 
of A being double that of B, the revolutions per minute of 
both the same, the linear velocity in A would be double that 
of B, and from this cause the resistance would be as the square. 
In A the area acted on would be four times as great as that 
of B, or as the square of the increase in dimensions ; thus we 
should have four times the resistance acting on four times the 
area in A, and therefore the effective resistance is proportional 
to the fourth power of the increase of dimensions. Also the 
resistance would be opposed at the end of an arm of double 
the radius ; so that finally the power-absorbing capacity of the 
dynamometer would be proportional to the fifth power of its 
linear dimensions. 

The operation of making a test with the machine is carried out 
thus. The boss of the turbine is bored out to a diameter larger 
than any shaft to which it will have to be applied and fixed 
to the shaft of the engine to be tested by means of an “ adapter ” 
which fits both the shaft and the boss of the turbine. The 
turbine so mounted will run true on the engine or propeller 
shaft. In the case of testing the engines of a ship the machine 
is attached to the shaft when the ship is in dry dock, 
and the casing connected to a supply of water which flows 
through the machine slowly and keeps down its tempera- 


106 


DYNAMOMETERS 


ture. By attaching a lever to the casing so that the ratio of 
the pressure at its outer end is as 1 to 10 a convenient 
pressure at the end of the lever can be dealt with ; the force 
at the end of the lever acts on a horizontal flat steel spring 
supported at its ends, such that its maximum deflection is 
about 1J inches. 

Experiments extending over many years have shown that 
for large loads the flat steel spring is greatly superior in 
constancy of action to the spiral spring, but recently spiral 
springs of excellent quality have been produced by a new 
process for purposes of weighing. But to return to Froude’s 
paper : the movement of the end of the lever is communicated 
to a bell-crank lever, to the vertical arm of which a long con¬ 
necting-rod is attached ; to this is fixed a recording pen, 
which moves freely along a sheet of continuous paper which 
derives its onward motion from the engine shaft. Also a 
stationary pen traces a zero line, such as the lever pen would 
trace when at no load. The area of the diagram is the product 
of the moment on the casing and the speed of the shaft, 
or the work delivered by the shaft. The lever is also 
connected, if desired, to an integrating apparatus of the 
Ashton and Storey type. My own experience has led me 
to use, whenever possible, the diagram method of recording 
work, since the diagram shows not only the total work done 
between fixed limits, but it shows how the work is developed 
at each instant. 

Either record by the addition of a time trace (usually made 
by a pen controlled by a clock) can be converted from a record 
of work to that of horse-power . In the machine described the 
excellent method of carrying the recording apparatus on points 
immediately over the supports of the ends of the spring ensure 
it against any external movements. A perfect trace is thus 
obtained, the ordinates of which are strictly proportional 
to the deflection of the spring, apart from any deflection of the 
frame by which it is carried. While the records are being 
made by the apparatus series of indicator diagrams taken from 
the engine give the indicated horse-power, and these when 
compared with the diagrams of brake horse-power show the 
amount of power expended between the cylinders and the end 
of the shaft. This difference or waste of power would exist 


WATER BRAKES 


107 


when the engines were propelling the ship, with the exception 
of friction due to thrust and a difference of friction on the 
bearings due to the propeller compared with that produced 
by the weight of .the water dynamometer. Both of these 
items can be corrected by calculation. 

The extinction of, say, 2,000 horse-power is accompanied 
by the heating of the water in the casing, and it has been 
shown by the author of the paper that the temperature 
would be kept below the boiling point of water if in each 
minute 8 cubic feet of cold water replaced the same amount 
of hot water in the casing ; this passage of the water would 
in no way interfere with the dynamometric action of the 
apparatus. 

It is almost necessary, even at the present date, to state 
in detail the great advantages which may be derived from 
the exact dynamometric tests of all classes of engines and 
prime-movers. There is a certain rather large and unknown 
quantity of power expended in friction which with the results 
of compression and release are very difficult to estimate 
by any method other than the dynamometric one. William 
Froude incorporates in the quotation I give here the real and 
important function of the test to be considered in this book. 
When discussing the difficulties which arise in three cases 
connected with ship propulsion, he writes 

“ (1) The speed attained by a given ship, driven by a given indi¬ 
cated horse-power, fails to measure discriminatively the merits of 
the ship. 

“ (2) No means exist of ascertaining which type of engine delivers 
the largest proportion of the power that it indicates. 

“ (3) No test exists by which it is possible to measure concisely 
the specific constructional merit of this or that engine, or to determine 
the relative constructional merit of the engines supplied by different 
firms. 

“ The dynamometric test would remove at once each of these diffi¬ 
culties by substituting a final and real test for a collateral, and to a large 
extent delusive, one. For to rely exclusively on the test furnished by 
the indicator is almost equivalent to testing the power of a horse solely by 
the quantity of food he consumes and digests, or the efficiency of a 
boiler solely by the quantity of coal per hour it will legitimately con¬ 
sume on its fire-bars.” 


108 


DYNAMOMETERS 


% 


The following explanation (which has been slightly abbre¬ 
viated) was given of the way in which current-growth was 
generated in the cells of the machine. Imagine (Fig. 51) a jet 
of water issuing at A with a velocity of 10 feet per second, to be 
caught by a fixed curved tube BC of the same diameter as A 
bent to a semicircle ; the water would enter B at 10 feet per 
second and also leave B at the same velocity, and in passing 
round the bend from its centrifugal force would set up a pressure 
tending to move the bent tube away from the jet. Next 
imagine the bent tube to move as shown by the arrow D at the 
rate of 1 foot per second ; then the water would be entering B at 
11 feet per second relatively to the bend, and would leave the 
bend at this velocity relatively to the bend, but at 12 feet per 
second with respect to any fixed point ; so that the forward 
motion of the bend at 1 foot per second would accelerate the 
flow at C by 2 feet per second. Now if the water leaving C 
entered a fixed semicircular bend, it would travel through this 
bend at 12 feet per second, and it might be again accelerated by 
passing through a second moving bend ; and so on ad infinitum, 
that is, if it met with no resistances due to friction of any kind. 
In this illustration we may regard the moving bend to represent 
a half-cell of the turbine approaching a half-cell in the casing, 
so that as the water was discharged from the cells of the casing 
into those of the turbine it was subject to a constantly-in¬ 
creasing acceleration, which is only balanced by resistance due 
to friction in the cells equal to the speed-producing power. 
The force resisting the rotation of the turbine equalled the 
resultant, in the plane of rotation, of the centrifugal force due 
to the current as it traversed the curved contour of the turbine’s 
cells ; this equalled the force exerted on the cells of the casing 
in an opposite direction. 

The Froude Water Brake Dynamometer (by Messrs. 

Heenan and Froude, Manchester : Figs. 52 and 53). 

The principle involved in the action of this dynamometer has 
already been described. It will be remembered that vortex 
motion is established in each cell of a turbine of peculiar con¬ 
struction and maintained by its rotation. Since the heat 
produced by the work done on the water is considerable, cold 


WATER BRAKES 


109 



water has to be introduced, but in such a manner as not to 
disturb the vortex motion. To effect this water is admitted 
through the fixed vanes of the turbine to points situated in the 
centre of the vortices, where both the pressure and the velocity 


Fig. 52 . 



















110 


DYNAMOMETERS 


are low. The lodgment of air is prevented by the water being 
introduced at a pressure of between 15 lbs. and 20 lbs. per square 
inch. The supply of cold water comes from a channel behind 
each set of the fixed vanes, and the hot water escapes into the 
outer part of the casing, leaving it by an outlet pipe placed at 
the highest point to enable air or steam to get away easily. 
The balance of the casing is not affected by the external con¬ 
necting tubes, since they are flexible. The ability of the 
dynamometer to absorb power depends on the surfaces of the 



cells being as smooth as possible, so that the velocities of the 
water within the cells may be the greatest. In order that the 
power-absorbing quality of the machine may be under control, 
a thin metal shield can be interposed between the faces of the 
turbine and the casing so as to reduce the vortical action. By 
this means the power may be reduced to about one-fourteenth 
part of the maximum power ; and in modern machines the 
power may be reduced to about one-fortieth of the maximum 
at any particular speed. The weight of the casing is not carried 
by the shaft, but by antifriction rollers, which can be adjusted 
so as to bring the turbine shaft into exact adjustment with the 
shaft of the engine to be tested. The casing is furnished with 
a lever weighted at its end with a weight greater than that which 
















WATER BRAKES 


111 


is actually required, the portion of the weight not lifted by the 
brake through the lever being supported by a small weighing- 
machine known as the Denison balance. The total load or 
effective weight on the lever equals the lever weight less the 
load indicated by the balance above the lever. Example :— 
Let the effective weight = W lbs. ; the radius of the lever = 
5 feet 3 inches ; revolutions per minute = N. The circum¬ 
ference of the circle of which 5 feet 3 inches is the radius is 
33 feet, so that 


Brake Horse Power = 


W x 33 x N 
33,000 


WN 

1 , 000 * 


It will be noticed that by making the radius of such a length 
that 27 tv = 33, the equation is made very simple and the pro¬ 
duct W X N has only to be divided by 1,000 to obtain brake 
horse-power. 

To set up the machine the turbine shaft is brought into line 
with the engine and coupled to it. Water is then turned on 
to the inlet pipe, air escaping from the outlet one. When the 
machine is in full action, the inlet valve is opened full, and the 
flow of water is regulated by the outlet valve, so as to keep up 
a certain amount of pressure in the casing. The water is 
retained in the casing by glands, the packing of which is in 
contact with the main shaft. Since the reaction against 
friction is in the same direction as that due to the water in the 
casing, no error is introduced by their employment. The 
quantity of water required to keep down the temperature is 
given by the formula 

r B.H.P. X 33,000 
U — 778 (T 2 — T x ) x 10' 

Where G is water in gallons per minute ; 

T x inlet temperature in degrees Fahrenheit; 

T 2 outlet temperature. 

This dynamometer possesses these qualities—namely, it can be 
applied to high-speed engines or motors, it absorbs very great 
power, while it can be regulated for any power within its range 
without the adjustment of weights. 


The Peter Brotherhood Fluid Friction Dynamometer. 

A hollow chamber, consisting of a shallow cylinder of which 
the diameter may be about twenty-two times the depth, is 





112 


DYNAMOMETERS 


carried on hollow trunnions ; these rest on antifriction rollers, 
carried by pillars on each side of the cylinder, which is called 
the casing (Fig. 54). Perforated annular plates are fixed to 
the casing, and between each pair a disc rotates, the discs being 
attached to a shaft which passes through the trunnions. The 
discs are close to the plates fixed to the casing, but do not touch 
them. When the discs are rotated frictional resistance is set 
up, which tends to rotate the casing. This resistance is 



Fig. 54. 

balanced by the moment of a force due to a spring balance, 
attached to a lever projecting from the casing. The energy 
imparted to the shaft and its discs is transformed into heat by 
the fluid friction, which heats the fluid. For a long test enough 
cold water must be supplied to the casing to keep the tempera¬ 
ture down to a convenient limit. The load on the motor at 
any required speed is adjusted by varying the quantity of 
water in the casing ; and any desired quantity of water may be 
retained, and consequently any load may be steadily main¬ 
tained, although water flows continuously through the casing. 




CHAPTER VI 


AIR BRAKES 


[Renard]. . 

[Morgan and Wood]. 115 

[White and Poppe] ........... 117 

[Logarithmic chart of air brake] . . . . . . . .118 

[Observations on air brake] . . . . . . . . .119 


The invention of the air brake is due to Messrs. W. G. 
Walker & Co. It was patented by Mr. Walker on February 4, 



1904, and numbered 2,743. In this form of ergometer energy 
is absorbed by means of rotating vanes, which set air in 
motion (Fig. 55). 

Two rectangular vanes are fixed on two radial arms, which 
are easily clamped on to the axle of the motor to be tested. 
Three different sized vanes are supplied with each ergometer. 
In order to make a test of a motor the ergometer is clamped on 
to the axle of the motor and the vanes are adjusted to such 
i). i 








































114 


DYNAMOMETERS 


a radial position that the motor runs at the required speed 
when under load. When the speed is known and the position 
and size of the vanes, the horse-power can be obtained from 
the calibrated results supplied with the ergometer. 

[There is an illustrated account of a Walker dynamometer 
of extra large size in the Engineer , March 24th, 1911, p. 297. 
With this the power absorbed at 450 revolutions per minute 
with the plates in their extreme inward position is 65 horse 
powder, while for the same speed at the extreme outward 
position it is 200 horse power. As the power absorbed varies 
as the cube of the speed, this machine at 1,000 revolutions 
per minute would absorb over 2,000 horse-power.] 

[Col. Renard made for some years experiments with an air 
brake, which he called Moulinet dynamometrique, for the 
purpose of absorbing and measuring the power of high-speed 
engines and electric motors. An account of his experiments 
is given in the Comptes Rendus de VAcademie des Sciences for 
May 2, 1904, and these are referred to at length in the work 
“ Dernier Evolution du Moteur a Gaz,” by Prof. Aime Witz, 
published by Louis Geisler, 1, Rue de Medecis, Paris, 1910. 
He employed a rectangular bar of ash which he could clamp 
crossways to the end of the shaft of the motor. The bar was 
divided from the middle both ways, and a pair of square alumi¬ 
nium plates were employed which could be secured to the bar 
in pairs at corresponding positions on either side of the axis. 
The plates were fixed so that the inner and outer edges of each 
were parallel to the axis of rotation and the plates were flat 
against the bar. He employed air brakes of different sizes 
according to the power required, and he established experi¬ 
mentally the following laws. With any particular combina¬ 
tion of bar and plates the resistance was accurately proportional 
to the square of the speed of rotation or the horse-power was 
proportional to the cube of this speed and also to the density 
of the air. For air brakes similar in form but of different 
dimensions the horse-power absorbed at any speed of rotation 
was proportional to the fifth power of the linear dimensions. 
With different positions of the plates on the bars the constant 
is determined by experiment. The author speaks of the great 
convenience of this form of brake and of the very large range 
of power which can be obtained with brakes of very moderate 


AIR BRAKE 


115 


dimensions. He draws a very rigid limit for the speed, which 
must on no account be exceeded on account of the risk of 
accident.] 

[An important investigation on the air brake has been 
made by Prof. W. Morgan and Mr. E. B. Wood, and a paper 
on the subject was read by them in June, 1913, before the 
Society of Automobile Engineers of New York. This is 
printed in the Proceedings of that society and a reprint will 
be found in the Proceedings of the Institution of Automobile 
Engineers (London) of 1914. The authors set out to investigate 
the laws governing the action of the air brake experimentally. 
For this purpose they employed a four-cylinder petrol engine 
to drive the brake, and in order to measure the power 
absorbed they mounted the engine and petrol tank like the 
motor of a cradle dynamometer, so that it could turn about the 
same axis as its own crank-shaft, being carried on large ball 
bearings for this purpose, and all balanced so as to be stable. 
The torque experienced by the balanced engine was measured 
as usual by means of a dead weight carried by an arm. The 
horse-power required to drive the fan at speeds varying in 
the ratio of over 2 to 1 or at powers of about 12 to 1 showed 
that the horse-power is accurately proportional to the cube 
of the speed, and this was found to be true with many sizes of 
plates at a number of different positions. 

An investigation of a rational formula for the resistance, 
depending on the size and position of the plates, is given, 
but these do not lead to results which can be relied upon as 
the cube law of resistance may be, and a tabulated constant 
is in practice necessary. A very important part of the experi¬ 
mental investigation relates to the disturbing effect of walls or 
screens near the fan. A number of rings which together consti¬ 
tute a disc could be separately or together fixed near to and 
parallel to the plane of rotation of the fan on one side only. 
These reduced the power absorbed, so that the power calculated 
by the formula suited to a fan in free space was higher than 
the actual power by amounts varying from 5 to 21 per cent., 
according to the number of rings. 

As screens were gradually built up close to and round the fan 
the excess of the calculated result became more and more, until 
when a rectangular box was built round the fan but open at the 

I 2 


116 


DYNAMOMETERS 


top the formula based upon free access of air gave a result 
194 per cent, too high, or nearly three times the correct amount. 
These show the great importance of allowing the fan to rotate 
in a clear space so that the air may circulate freely. 

Tests were made with the barometer at different levels, but 
the range was very inadequate for this purpose, being only 
from 29*9 to 30*7 in. Within this range, however, consistent 
results were obtained, from which the variation of resistance 
was found to be twice as great as the variation of pressure, and 
hence of the density of the air. This would correspond with a 
law making the resistance proportional to the square of the 
density for which there is no theoretical justification, and it is 
inconsistent with the experience of Col. Renard. I do not 
think, therefore, that the evidence for such a law is sufficient, 
and where the air brake is used in circumstances leading to a 
considerable departure of the density of the air from that 
obtained under normal conditions, as at high altitudes, where 
the barometer is always low, or where a low barometer and a 
high temperature or the converse cause the density to be 
abnormal, a correction should be made depending on the new 
density. The following table may be useful for this purpose : 


Table showing the number by which the power calculated 
from the constant of the air brake should be multiplied for 
different temperatures and pressures. 


Barometer 

(Inches, 

Mercury). 

Temperature (Fahrenheit). 


0 

20 

40 

60 

80 

100 

120 

25 

1-060 

1-107 

1-154 

1-200 

1-246 

1-293 

1-340 

26 

1-020 

1-066 

1-111 

1-154 

1-198 

1-242 

1-288 

27 

•983 

1-026 

1-069 

1-112 

1-154 

1-197 

1-240 

28 

•947 

•989 

1-031 

1-072 

1-113 

1-154 

1-196 

29 

•914 

•955 

•995 

1-035 

1-075 

1-115 

1-155 

30 

•884 

•923 

•962 

1-000 

1-038 

1-077 

1-116 

31 

•856 

•894 

•931 

•968 

1-005 

1-042 

1-080 

32 

•829 

•866 

•902 

•938 

•974 

1-010 

1-046 


Taking the density of air as 1 when the barometer is at 30 
inches and the thermometer at 60° Fahrenheit, the reciprocal of 














AIR BRAKE 


117 


the density at other temperatures and pressures are tabulated. 
These figures will show to what extent the power calculated 
from the cube of the speed and the constant is in error. This 
calculated power should be corrected by multiplying it by the 
number in the table to obtain the true power, i.e., if the standard 
conditions are those on which the constant of the air brake is 
based.] 

[White and Poppe Air Brake and Formula.] 

[In the Automobile Engineer for August, 1910, page 68, there 
is an article describing the White and Poppe testing systems. 



These engineers used the fan brake with square plates fixed 
with their centres at a distance r centimetres from the axis 
and with their outer edges r + a/2 = R centimetres from the 
axis as represented in Fig. 56, and, causing it to make N 
revolutions per minute, found as the result of experience that 
the horse-power could be obtained from the following 
equation :— 

a 2 x R 3 x N 3 

Horse-power = 4010,000,000,000,000' 

They do not give this as a theoretically correct formula but 
one which for practical purposes is useful. As no allowance is 
made for the bar to which the plates are fastened, and as it 
clearly cannot apply accurately to plates of absurd dimensions, 
the reader must not attach too much importance to the formula 
or employ it with plates and radius bars of unusual proportions. 
As within its limits this seems to be a useful expression, I have 

















Horse-Power. 


118 


DYNAMOMETERS 


calculated and expressed on the accompanying logarithmic 
chart (Fig. 57) the horse-powers for a number of sizes of plates 
all set with their middle points at 55 centimetres from the axis. 
Each size of plate is represented by one of the eleven parallel 



Fig. 57. 


straight lines. Where these intersect the vertical or horizontal 
lines of the chart the horse-power and number of revolutions 
per minute, represented by the points of intersection on the 
vertical and horizontal scales respectively, are those that, 
according to the formula, should be absorbed by the particular 
plate. For instance, at 1,000 revolutions per minute the plate 




























































































AIR BRAKE 


119 


20 centimetres square with its centre 55 centimetres from the 
axis should with the arm absorb 27-4 horse-power. As I have 
stated on page 26, the tangent of the angle which a line on the 
logarithmic chart must make with the horizontal to indicate 
the law y — x n is simply n ; n in this case is 3. As, however, I 
have used a horizontal scale four times as great as the vertical 
scale, so that the useful range shall be contained in a chart of 
convenient size, the tangent of the angle is changed to §. There 
is a line sloping the other way (not quite straight, as the 
resistance does not, according to the formula, follow a law 
which is any exact power of the size of the plate), which I have 
called a scale line, * the purpose of which is this. If the horse 
power corresponding to a square plate of any other dimensions 
than those for which lines are ruled should be required, it is 
merely necessary to follow along the scale line until it intersects 
a horizontal line the numerical value of which is that of the side 
of the new plate. At the point of intersection draw a line 
parallel to the lines corresponding to the other plates, and this 
line will give the corresponding values for the new plate without 
any calculation. For instance, it cuts the sloping 10 line at 10, 
12 line at 12, and so on. 

The single line, drawn at a steeper angle than the others, is 
made to slope at an angle whose tangent is f. It therefore 
indicates a fifth power law, and it may be used to find the scale 
of magnification of an air brake necessary to increase the 
resistance to motion for all ratios up to 1 to 10J or 10 to 105. 

If, then, the scale on which any actual air brake is constructed 
be called 1,000, then, following this line, it will be seen that as 
the scale is increased as indicated on the horizontal row of 
figures to 1,600 the resistance will increase in the ratio of 10 to 
105 as read on the vertical row of figures, or a tenfold increase 
of resistance may be obtained by increasing the dimensions in 
the ratio 1,000 to 1,585, i.e., so as to be very little more than 
half as big again in every dimension. As the fifth-power law 
is a true law, and is in no way dependent upon the empirical 
equation of White and Poppe, this line, or any line parallel to 
it, may be used with confidence.] 

[The simplicity of the air brake and its law of resistance 
leading to great stability of speed make this type eminently 
* Nature, July 18, 1895, J>. 272. 


120 


DYNAMOMETERS 


suitable for testing motor-car engines ; but it is necessary to 
bear in mind that the tabulated constants of the fan only apply 
accurately to definite conditions, and that where these are 
departed from, i.e., where walls or partitions are so near as to 
interfere with the proper air movements, the rated power will 
be in excess of the true power. Care also should be taken so 
to use the air brake that it may not cause accident or nuisance. 
If an air brake is used at a speed beyond that for which it has 
been designed, especially if rigidly driven by a high-speed 
petrol engine with one or two cylinders, where the constantly 
repeated and severe stresses due to variations of speed are added 
to those already in excess of the proper capacity of the structure 
this may lead to accidents of a very disastrous character. The 
writer prefers at any time not to stand in the plane of rotation. 
The noise caused by the whirring of the plates is not of much 
consequence in an engine-house, but this may lead to trouble 
in a residential neighbourhood, especially if they move close to 
framing, for this gives rise to a beating of the air which is 
peculiarly disturbing. It is evident that this type of brake 
does not admit of adjustment of its resistance while running as 
the electrical and liquid brakes do.] 


CHAPTER VII 


MAGNETIC BRAKE DYNAMOMETERS. 


PAGE 


Arago’s observation 
Foucault’s observation . 
Violle’s measurements . 
Morris and Lister . 


. 121 

. 122 


. 122 

. 122 


In 1824 Arago, a Frenchman great in physics, found that 
when a disc of copper was rotated under a magnetic needle 
supported on a needle point above it situated in the axis of 
rotation of the disc the magnetic needle followed the rotating 
disc in its direction of rotation after a certain speed was 
reached. The rationale of this experiment was given by 
Faraday,* who showed that the phenomenon of Arago was 
due to magneto-electric induction. Babbage and Herschel'j* 
investigated the matter and showed that the effect could only 
be produced with metals, while Arago held that the effect 
takes place with solids, liquids, and gases. Faraday was 
working on this phenomenon in order to discover the true 
interaction between the copper disc and the magnetic poles. 
He rotated a copper disc between the poles of a magnet, 
connecting the centre of the disc and the edge of the disc 
through a rubbing contact with a galvanometer. On rotating 
the disc Faraday found that a current was generated, and that 
the deflection of the needle of the galvanometer showed that 
when the direction of rotation was changed the direction of the 
current was also changed. Thus the first true dynamo was the 
outcome of this excellent experiment of Faraday. The peculiar 
feature of this prototype of the family of Dynamos is that the 
current is absolutely continuous, but from the nature of the 
arrangement the potential difference between the centre of the 


* “ Experimental Researches in Electricity,” Vol. I. 
| Phil. Trans., 1825, p. 467. 





122 


DYNAMOMETERS 


disc and its edge is very small. Foucault * devised an experi¬ 
ment by means of which the heating effect of internal currents 
(now called eddy currents) generated in a copper disc rotating 
in a magnetic field might be estimated, but Violle f was the 
first to estimate the work required to rotate the Foucault disc 
and thus heat it. This was a real ergometer experiment, made 
on the gravity method already mentioned. From this he 
deduced the heat equivalent as 435 kilogram-metres, a result 
too great when compared with the value 428 found by Joule. 

This behaviour of a copper disc in a magnetic field is taken 
advantage of in the construction of galvanometers of the 
magnetic-needle type ; the needle swinging over a copper disc 
induces currents in the copper which react on the needle and 
tend to bring it to rest; [also in electric motor meters the same 
interaction is utilised in order to obtain a resistance strictly 
proportional to the speed of rotation. Then, if the torque 
causing the disc to turn is made proportional either to the 
current strength or to the current energy, the rate of turning 
of the disc will be proportional to one or other, and the number 
of turns recorded on the dials will be a measure of the 
integrated current or energy, as the case may be.] 

The Foucault phenomenon has been utilised by Messrs. 
Morris and Lister in the construction of an absorption ergo¬ 
meter, in which the eddy currents produced in two copper 
discs by a magnetic field generate a torque by their reaction in 
that field. This machine, which is called by the inventors an 
“ Eddy current testing brake,’’ is described thus by the 
inventors :— 

“ The Brake consists of two copper discs each mounted on a cast 
aluminium spider. These are made fast, one at either end of a sleeve 
which is keyed to the shaft of the motor under test (Figs. 58 and 59). 
Riding loose on this sleeve and between the two copper discs is an 
aluminium casting carrying a number of electromagnets, wound so as 
to have alternate polarity. These magnets consist of well-ventilated 
coils on circular cores fitted with pole pieces. To the outside of each 
copper disc is secured a ring of wrought iron, which revolves with the 
copper and at the same time forms a path for the magnetic flux. These 

* Foucault, “ Annales de Chimie et de Physique,” 3me serie (1855), T. XLV., 
p. 316 ; and “ Recueil des Travaux scientifiques de Leon Foucault,” p. 342 Paris* 
1878. 

f Violle, “An. de Ch'm. et de Phys.,” 4me s£rle T. XXI. (1870). 


ERGOMETERS 


123 



iron rings are fitted with cooling vanes, which dissipate the heat gene¬ 
rated. When the motor is running the magnetic flux in traversing the 
moving copper induces eddy currents, which absorb the energy of the 
motor in heating the discs. At the same time the flux tends to drag 




















































124 


DYNAMOMETERS. 


round the magnet system and levers. By suitably adjusting the 
exciting current the lever floats. The power is then given by— 

_ . . Torque in lb. foot units x revolutions per minute 

Brake horse-power =- - -5250- 

“ This force tending to turn the field magnets round is opposed by a 
gravitational force, due to a weighted lever. When these two forces 
are in equilibrium the lever floats between stops, in a horizontal position. 
The weight is so placed that when the lever drops below the horizontal 
position, the effective radial distance of the weight is reduced, and if 
the lever is above the horizontal the effective radius is increased, but 
when the lever is horizontal, the weight acts at a definite measured 
length of lever to which it is adjusted. In the horizontal position of 
the lever the exact value of the moment of the weight about the axis 
is a known quantity.” 






CHAPTER VIII 


END THRUST BRAKES 

PAGE 


Bourdon.125 

Jervis-Smith ..125 


The work-measuring machine of Bourdon (before 1870) is 
curious ; its construction appears to differ entirely from that 
of any other work-measuring machine. 

Two helical toothed wheels are in gear—one is driven by a 
belt by any motor, the other helical toothed wheel transmits 
the motion to the machine driven and under test. But, from 
the nature of the gear, the force acting in the plane of rotation 
has a component along the axis. Let the angle made between 
the slope of the teeth and the axis be fi and P the pressure 
between the teeth in the plane of rotation, then the pressure P x 
tending to move the wheel along the shaft is P x = P tan /3. 

This end pressure acts on a spring connected to a pointer, 
the deflection of which can be read on a dial. When the 
distance traversed by the point of application of the force is 
known per unit of time, and also the force, the power trans¬ 
mitted is at once determined. 

The following description of an ergometer by the author is 
taken from a pamphlet on work-measuring machines (E. and 
F. N. Spon) published in 1884 :— 

“ A torsion ergometer (Fig. 60). This form of ergometer is very 
different from any already described. It was used to control the 
motion of a dynamo worked by a windmill; the first windmill to which 
this arrangement was applied was nearly destroyed by the storms of 
September, 1882, at Taunton. Since then the plan of placing the 
dynamo in the head-cap of a windmill, thus avoiding the introduction 
of long shafts to bring down the motion, has been found to answer well; 
the conductors alone are brought down, the connection with the head- 
cap being made through rubbing contacts of copper on rings of the same 
metal. The wheel B is attached to the pulley A by means of two links 




126 


DYNAMOMETERS 


LL, as shown at KMN. The wheel A is fast on the shaft CD, and B is 
loose. If B be turned as shown by the arrow on the belt M the tendency 
of the links is to make the pulley B approach A and thereby compress 
the spiral spring S. A gun-metal wheel E, kept by means of a spring 
against the disc F, which is part of the pulley, moves a pointer over the 
dial H, and thus the tension of the belt at the effective radius is read. 
A speed indicator is attached as in the other machines. The central 
spring at the end where it comes in contact with the pulley B is furnished 
with a sleeve which slides on the central shaft. The end face of the 
sleeve is grooved, and the part of the pulley opposite to this groove is 



also grooved in a similar way. Several steel balls are placed between 
the grooves and render the contact between the spring and the pulley 
as frictionless as possible. The pulley B has a larger face than A, to 
permit of the slight side motion necessary to act on the spring.” 

In 1884 I devised and made an ergometer in which the 
tension of a belt was shown by the lateral shifting of one of two 
pulleys mounted on a shaft. The driven pulley was keyed to a 
shaft, while the loose pulley was connected to the fixed pulley 
through two rollers bearing on two spiral inclines which formed 
a part of the fixed pulley. The effect of increasing torsion 
between the two pulleys was to cause relative displacement and 
thereby compress a spiral spring. The axle of the machine was 



















END THRUST BRAKES 


127 


tubular and the spiral spring pressed against a sleeve, connected 
through a slot in the axle with a cylindrical block within the 
axle ; in this block a rod, projecting outside the axle, was free 
to rotate and actuate a pointer which indicated the difference 
of the tension of the belts on the two pulleys. The spring 
acted on the boss of the loose pulley, through a sleeve pressing 
against the boss through antifriction wheels. The loose pulley 
was wider over the face than the fixed one to allow for its small 
lateral displacement when running. The machine ran well and 
had practically no tendency to “ hunt.” 


CHAPTER IX 


HISTORICAL 

PAGE 

Coulomb..1^8 

Prony on Coulomb ....••••• • 131 

De Borda ] 

Marey l (Stream Lines).. .133 

[Hele Shaw] J 

[Froude’s lecture at the Royal Institution] . . . . . .139 

[Osborne Reynolds and critical velocity] ...... 142 


[Memoires de PInstitut National des Sciences et Artes, Coulomb 
(Science, Math, et Phys.), T. II.] 

In this memoir I have been principally engaged in deter¬ 
mining to what degree a load more or less great is capable of 
diminishing the power (quantite d’action) which a man is able 
to yield in a day’s work. The experiments which have been 
utilised on which to base that determination have been made 
in conformity with the most natural and common movements 
of men, such as walking horizontally, or ascending a flight of 
steps. The evident result appears to me to be that a man who 
ascends a flight of steps freely, and without any burden, is 
able to yield an amount of power nearly double that which the 
same man can yield when loaded with a weight of 68 kilograms, 
which is about the average load of men who carry up wood in 
houses. But since in that way of employing strength there is 
no useful work done besides the raising of the load, the result is 
that the useful work done by a man who ascends is not more 
than one-fourth of the total quantity of work done which a man 
yields in a day who ascends a flight of steps in the ordinary 
manner, and, allowing himself to fall, raises, by some means, a 
weight equal to his own weight. He will then produce nearly 
the same effect, or will do the same amount of work, as four 
men carrying similar weights on their backs. This observation 
appears to be of the greatest importance in guiding mechanicians 
in the construction of machines to be moved by men whose 



HISTORICAL 


129 


power should be always employed in the most advantageous 
manner in producing useful effects. I further sought to 
compare the total quantity of power that men could yield in 
freely ascending a flight of steps with that which they gave 
when working in ringing a bell, or working a winch, etc., and I 
found that a man who ascended freely, i.e., without a load, a 
flight of steps could do at least twice the amount of work that 
could be done in other modes of using their strength. The 
experiments which served to base the determination of the 
quantity of power used in the case of the bell and the winch 
were always made in the large workshops. I would ask those 
who may wish to repeat the experiments, if they have not time 
to measure the results after many days of continuous work, to 
observe the workman at different repetitions of their work 
during the day without the men knowing that they are watched. 
One cannot be too much warned of the risk of being deceived 
in calculating either the velocity or the effective period of work 
after a single observation of some minutes’ duration. The 
results of all the preceding sections make the values for power 
much less than those made use of by the majority of authors 
in the estimation of machines ; but the latter have been nearly 
all based on experiments which lasted some few minutes, and 
have been carried out by men chosen for the purpose ; the 
calculations based on experiments, therefore, have been 
established on the supposition of effective work having been 
carried on for seven or eight hours per day. But in nearly 
every kind of work a man could put forth during some minutes 
an amount of power double or even treble his mean rate of 
doing work ; he could even condense his whole day’s work 
into two or three hours. This is what we have seen in the 
preceding section, where men who carry wood concentrate all 
their day’s work into the time that they are subject to the 
load, and this is not more than one and a half hours during the 
day’s work. The choice of men again greatly influences the 
determination of their mean strength. I have observed during 
ten years the carriage of earth moved by troops and by work¬ 
men, by the toise cube, as it is commonly called [toise = 6* 39 feet]. 
I made fortnightly measurements, and found nearly always 
that the workmen belonging to the Grenadiers had gained by a 
third over the other companies, and often by a half over feeble 
D. ' K 


130 


DYNAMOMETERS 



Rate of doing 

work in h.p. 

0*128 

0*0473 

Quantity of 
work done per 
day’s work. 

foot-pounds. 

2,030,400 

561,600 

Time during 
which work was 
done per day. 

hours. 

8 

CO 

Work done 
per second. 

foot-pounds. 

70*5 

26 

Velocity or path 
traversed per 
second. 

feet. 

0*49 

0*65 

Weight raised or 
stress brought 
into play. 

. CO 

co 

£ rH 

co 

ds 

CO 



r ' 


a 

o 

X 

f-i 

O 

ir 


eS 


<£> CO GO 

Ph'S 'S 

r ~ac> _ r- &D 

0 

a> c® 

1 —i o co 

■+3 *I-H 

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43 ° 
bJD 2 <3 

*3 .*£ +=> 

h3 S • 
3 ^ 60'S 
a> 3 r Bs 

o r/ r • ^ W) 

S 

§ “ g g 

s o Is o 
<1 


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£ fH 

.g a> 

£ ^ 

QD 4 * 3 

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p £ £* 

'55 ^ pH 

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fH g 0) 
o c« tjo 

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HISTORICAL 


131 


workmen. If I had determined the mean strength of all the 
individuals who formed the workmen of the Grenadiers I 
should have found it a third greater than the mean strength 
of other workmen. It is true, and it must be remarked, that 
in this kind of work, of which the greater part consists in the 
wheeling of earth, not a single weak man is found amongst the 
workmen of the Grenadiers, and that two or three bad work¬ 
men amongst each of the other sets of workmen diminish the 
whole work done. 

In conclusion, a variation of the mean quantity of power is 
due to food, but above all to climate. I have executed great 
works at Martinique carried onby troops—temperature 20 °C.— 
and I have also executed with soldiers the same kind of work 
in France, and I am sure that in this 14th degree of latitude, 
where the men are nearly always bathed with perspiration, 
the men are not capable of doing half the work that they can do 
in our climate, i.e., in the climate of France. 

Prony on Coulomb. 

Results of many experiments devised to determine the power 
which men can yield in their work during a day, taking 
into account the various ways in which their strength is 
employed, by C. Coulomb. 

Note on the memoir of Coulomb by Prony. 

In order to give a clear and precise summary of this interest¬ 
ing memoir, it is necessary in the first place to determine the 
meaning of the words “ quantity d’action” 

The effect which results from the mechanical work of men 
should always be reduced to raising of a heavy body ; the 
velocity, moreover, with which this movement has been 
generated will die out if the cause which produced it shall 
cease to act, and it is necessary that a man should make a 
continual effort on the body to keep up that velocity. Here 
we have, then, two quantities which may be stated in numbers : 
the velocity, which is the number of metres or units of space 
traversed uniformly in the unit of time ; and the stress (effort), 
which may be expressed and measured by a certain number of 
kilogrammes or units of weight. The product of these two 


132 


DYNAMOMETERS 


numbers represents and measures power (action), and when 
multiplied by the third number, viz., the time during which 
the stress acted, gives the quantity of power, or the total 
resultant effect of work, and it thus ranks as one of the things 
which may be measured and are susceptible of calculation. 

Furnished with such information, the fundamental object of 
experiments is the comparison of the work done with the 
fatigue which necessarily follows it. The same quantity of 
work (or the number which expresses it) may result from an 
infinite number of different combinations of values of numbers, 
the product of which serves to measure it, combinations 
which depend on the different methods of utilising human 
strength. Is the fatigue, then, equal, in all cases, for the 
quantities involved for equal work, or does it vary under 
different circumstances, or does it cause the numbers which 
represent velocity, force, and time to vary ? 

Daniel Bernoulli and other celebrated authors have adopted 
the former opinion ; but Coulomb showed that they had 
deceived themselves, and while he overthrew an error empha¬ 
sised by such weighty authorities by means of proofs drawn 
from reasoning and experiment, he has done great service to 
applied mechanics. 

Nevertheless, although fatigue may not be simply propor¬ 
tional to the quantity of work, it is a function of it—that is to 
say, the formula which represents it should comprehend, in 
some way, velocity, force, and time. 

One knows, from the theory of mathematical analysis, that 
there must exist a certain relation amongst these three things 
such that a given effect may be produced with the least fatigue, 
or that with an equal fatigue the quantity of action or total 
effect may be a maximum. This is the problem which the 
author has proposed to solve, and which he has investigated 
in the different methods of utilising the exertion of man. He 
examined firstly the quantity of work that men were able to 
yield when they ascended, during a day of work, a slope or a 
flight of stairs with a load or without a load. The experiments 
which he cites on this point prove, to begin with, the inaccuracy 
of the opinion of Bernoulli ; he found that the quantity of 
work done by a man who ascended without a load, or who 
had only to raise his own weight, is double that of a man 


HISTORICAL 


133 


loaded with 68 kilos, (each man working through a day), the 
weight of his own body being included. One sees then in a 
striking manner how, for equal fatigue and during a given time, 
that the total or absolute effect produced assumes different 
values through different combination of force and velocity. 

But the word “ effect ” means here the whole quantity of 
work done in raising both the load and the weight of the man ; 
and that which it is important to consider is the useful effect, 
that is to say, the whole effect, deduction being made for the 
value which represents the moving of the weight of the body 
of the man. This effect is the greatest possible when a man 
ascends without a load, but then the useful effect is nil; it is 
also nil if a man is burdened with a load so great that he can 
hardly move. There exists then, between these two limits, a 
value for the load such that the useful effect is the greatest 
possible. Coulomb supposed that the loss of the quantity of 
force is proportional to the load (an hypothesis which experience 
confirms). It furnishes an equation which, treated by the 
rules of maxima and minima, gives 53 kilos, as the load 
with which a man should be burdened, so that he may obtain 
the greatest useful effect in ascending a flight of stairs during a 
day’s work. 

And the quantity of work which results from this determina¬ 
tion, and which amounts to 56 kilos, raised through the height 
of one kilometre, is sensibly the same as that given by experi¬ 
ment. But this method of doing work causes three-fourths of 
the total work to be lost, and consequently the cost of work 
under such conditions costs four times as much as when, in 
working, a man ascends a flight of stairs without any load, 
and then, allowing himself to fall, raises by some device a 
weight nearly equal to his own. 

(The man descends on a seat attached to one end of a rope, 
which runs over a pulley, the other end being attached to the 
load.—F.J.J.S.) 

“ On the Flow of Fluids from Orifices in Vessels,” by Monsieur 
le Chevalier de Borda. [Mem. de l’Academie Royal, 
1766.] 

I again take an example from the theory of the resistance 
of fluids,' of the bad use one may make of this principle. We 


134 


DYNAMOMETERS 


know that, in order to give a general solution of the problem 
of the resistance of fluids, one supposes a body D (Fig. 61) 
fixed in the midst of a fluid of indefinite extent, having a 
uniform motion in a straight line ; 
we imagine, in addition, that the 
molecules of fluid, when approach¬ 
ing the body D, describe curved 
lines, abed , etc., efgh, etc., or 
for the most part move in little 
curved canals abed, efgh, etc., 
and one seeks to determine by the 
conditions of the problem the form 
of these little canals as much as 
the resultant pressure against the 
body D ; but it is easy to see that 
each of these little canals necessarily 
has a portion bf, more narrow than 
the hinder parts d h, etc., which 
therefore may be classified with 
symptoms which we have mentioned 
in the preceding section; one need 
not employ in the case of this sort 
of movement the principle of the 
conservation of “forces vives ” ; but 
independently of the general proof 
there is one thing peculiar to the 
theory of the resistance of fluids ; it 
is that in using, without restriction 
in that theory, the principle under¬ 
lying it the result of the calculation 
will give a resistance equal to zero 
(une resistance nulle). To show this, 
suppose that the body D moves 
uniformly in a fluid at rest, drawn 
along by the action of the weight P : 
one knows, following the principle, 
the difference between the “force vive ” of the fluid should be 
equal to the difference of the effective descent of the weight P : 
but when the movement has become uniform, the difference of 
the “forces vives ” = o ; therefore the difference of the effec- 



lip 


HI!! 

■ill 

'jii! ! j 

i i i J i! 1 

i iijihi 

liipji 

Iliii illii 

i!|iijl| 

Ijjjiiiijii 

jl i! iliii 

liijis!! 

! 1 ! i i 

]!!!( ij !jj 

Ijiiijii 
! SiiDi 

Uiiliiiinil 

iiiiiih 


II 

!if 


ill! 


h>i! 










HISTORICAL 


135 


tive descent will = o. The weight then indicates the resistance 
of the fluid ; therefore the supposition of the principle which 
is at stake always gives a zero resistance. 

“ The Movement of Air Studied by Means of Chromophoto¬ 
graphy,” by M. Marey (Bulletin des Seances de la Soc. 
Frangaise de Physique, Seance du 17 Janvier, 1902). 

In this research on the movement of air M. Marey has made 
some beautiful and excellent experiments whereby the move¬ 
ments of air as it flows are clearly exhibited. The lines of 
flow of liquids such as water have been made known by the 
introduction of small streams of coloured matter, such as 
aniline dye. The method was employed by Prof. O. Reynolds, 
in his work on the flow of water through tubes (see page 142), 
and recently Prof. Hele Shaw has shown by means of streaks of 
coloured matter the lines of flow of a liquid, projected on a 
screen. M. Marey has dealt with the time measurements of 
the movements of a liquid by allowing the liquid, e.g., water, 
to hold brilliant little bulbs of the same density as water in 
suspension, the bulbs being illuminated by bright sunlight. 
When obstacles of different forms are placed in water flowing 
by with the bulbs in suspension the lines of flow are at once 
evident. In one experiment the stream lines are shown as the 
water flows past a plane inclined to the original line of flow. 
The stream lines separate, some flowing to the right and some 
to the left, from a point which appears to be the centre of 
pressure. [Not only were the directions of flow made clear, 
but the speed at every point. With this object the illumina¬ 
tion was made intermittent at the rate of ten flashes per 
second. The lines photographed were then beaded and the 
wider or closer spacing of the bright points in relation to a 
scale of millimetres gave the speed at every point.] M. 
Marey, going a step further, has produced some clear photo¬ 
graphs of the flow lines of air. It would be nearly impossible 
to imitate the former method as used in the case of water and 
float minute balloons in air, but his excellent results have 
been obtained by introducing threads of smoke into air as it 
flows through a tubular chamber. 

[The stream of air was drawn regularly through the experi¬ 
mental trough, and to ensure regularity was passed through two 


136 


DYNAMOMETERS 


frames over which silk gauze of extremely fine and regular 
texture had been stretched, one at the entrance and one at the 
exit of the trough. The smoke, which was produced by 
burning tinder, was led by a number of very thin and parallel 
tubes to the surface of the inlet gauze. The streams of smoke 
remained sharp and separate throughout the length of the 
trough. They were photographed by an instantaneous flash 
of magnesium light. When any obstacle such as an inclined 
plane or a ship-shaped body blunt at one end and sharp at the 
other was introduced the new lines of flow were clearly seen 
and the extent of the disturbance was shown to be greater, 
indicating greater resistance if the blunt end were at the down¬ 
stream end than it was if this were meeting the flow, in agree¬ 
ment with the forms of birds and fish and also of ships. When 
it was desired to obtain the speed at all parts of the stream 
lines the system of fine smoke tubes was kept vibrating by an 
electric trembler at ten vibrations per second. The lines then, 
whatever their form, had superposed upon this a fine ripple 
pattern, and the distance of consecutive waves in relation to a 
millimetre scale gave the velocity of the stream at all parts of 
the photograph.] 

[The author included in his Table of Contents a reference 
to Prof. Hele Shaw’s experiments on stream lines. These are 
described in the Transactions of the Institution of Naval Archi¬ 
tects, Yols. XXXIX. and XL., the British Association Report, 
1898, and in the Transactions of the Royal Societv, 
Vol. CXCV., A. 

Prof. Hele Shaw first made experiments on stream line 
motion past obstacles, rendering the motion visible by a froth 
of air bubbles included in the liquid. The air-bubble method 
was soon superseded by streaks of coloured liquid. The special 
feature of Prof. Hele Shaw’s experiments was the use of an 
extremely thin lamina of fluid included between glass plates, 
and he used liquids differing so much in viscosity as water and 
glycerine. Sir George Stokes, who had seen Prof. Hele Shaw’s 
results, showed (British Association Report, 1898) that a 
viscous liquid moving in an extremely thin sheet, though 
wholly different dynamically from a perfect or frictionless 
fluid moving in three-dimensional space, but with two- 
dimensional flow (obstacles being supposed in this case to 


HISTORICAL 


137 


be indefinitely extended in a direction normal to the plane 
of flow), nevertheless had stream lines identical in form, so 
that* experiments on viscous fluids in narrow channels could 


Fig. 62. 

safely be used for ascertaining the forms of stream line flow of 
a frictionless fluid in two dimensions. Prof. Hele Shaw verified 
this experimentally in certain cases capable of being examined 
mathematically, and so was enabled to determine the forms 






















138 


DYNAMOMETERS 


of stream line motion in other cases not susceptible of mathe¬ 
matical treatment. These experiments reached their highest 
development in the research described in the Royal Society 



Fig. 63. 


paper referred to above. The object is to find the solution of 
the forms of magnetic lines of force in a variety of cases. Here 
instead of an obstacle bodies of higher permeability than that of 
the surrounding medium are interposed. These allow magnetic 
induction to take place more freely through them and so are 










































HISTORICAL 


139 


imitated by the use of slides in which the narrow space occupied 
by the moving liquid has places of greater depth of the form 
of the more permeable body. The resistance to flow is inversely 
as the cube of the thickness of the layer, so the deeper portions 
represent greater permeability and any particular permeability 
may be imitated. The accuracy of this way of imitating 
permeability was verified by experiments with elliptical and 
circular depressions, the effects of which could be calculated, 
and so it was possible to get valuable information as to toothed 
armatures and other forms not amenable to mathematical 
treatment. It would be going too far from the subject of 
this book to give particulars of the singularly perfect arrange¬ 
ments made use of in this investigation, but as the results 
are so exquisite, and as they represent the highest perfection 
known to the writer yet reached in recording stream line 
motion, I am glad to be able with the permission of the Royal 
Society and of the author to reproduce two of the photographs. 
The first (Fig. 62) shows an ellipse of permeability 20 in a 
uniform magnetic field, while the second (Fig. 63) shows the 
screening effect of a hollow circular cylinder upon a square 
prism both of permeability 100 in a uniform magnetic field. 
It is hardly possible to believe that the dark and light bands 
are actually moving liquid and that they should contract, 
keep distinct, and widen again symmetrically as they do 
without losing their sharpness.] 

[William Froude’s Lecture.] 

[The author left a reference to the interesting lecture 
delivered by William Froude, F.R.S., at the Royal Institution 
on May 12, 1876, and as this appears in his Table of Contents 
I have thought it desirable to give an indication of the subject 
treated. The true causes of the resistance of ships, depending 
on skin friction, eddy motion, and wave-making, were explained 
while the absence of any resistance due to obstruction equiva¬ 
lent to a pressure over the transverse section was shown in a 
series of propositions on stream lines, at least for an immersed 
body, to be wholly absent even though so plausible a theory 
had been universally accepted in past times.* 

* De Borda’s paper (p. 134) appears to have been overlooked. 


140 


DYNAMOMETERS 


(1) A plane surface moving edgeways through a frictionless 
liquid obviously meets with no resistance. 

(2) A plane surface moving edgeways through a real 
liquid such as water meets with a resistance called “ skin 
friction.” 

(3) A submerged body moving through a .frictionless but 
heavy liquid should under the plausible ideas of the past meet 
with opposition, but the stream line principles to be indicated 
after the skeleton argument shows convincingly that there 
can be none. 

(4) A submerged body moving through a real liquid is 
subject to skin friction, depending upon the extent of its 
surface and speed, such as might be obtained by drawing a 
sheet of the same total area edgeways at the same speed. 
It may also suffer from some small resistance due to eddies 
in the wake if the stern end is too blunt. There is no resistance 
due to obstruction acting over the cross-section. 

(5) A floating body moving through and partly immersed 
in a frictionless liquid will, especially at higher speeds, generate 
waves the energy of which is derived from the motion of the 
body. This represents resistance. 

The waves are formed because, as the stream line theory 
shows, the presence in the water fore and aft (at least in the 
case of ship-shape bodies) is above the normal, while it is 
below the normal amidships. The surface level of the water, 
therefore, is higher fore and aft and lower amidships. A wave 
travels at a definite speed, depending on and in proportion to 
the square root of its wave length. When the floating body 
approaches the speed at which the wave due to its motion 
also travels, the wave-making effect becomes greatly increased 
and the resistance rises rapidly. At much lower speeds wave¬ 
making is almost non-existent and the resistance is very small. 
If the floating body could be accompanied by a mechanism 
which would hold the water surface level and prevent the 
formation of waves, then the conditions of an immersed body 
would be met with and the resistance would vanish. 

(6) A floating body moving through and partly immersed in 
a real liquid experiences a total resistance which is made up of 
all three—viz., skin friction, eddies in the wake, and wave- 
making. At low speeds the skin friction only is important; 


HISTORICAL 


141 


the friction due to eddies in the wake is a small fraction of 
this. These two each increase in a rather higher proportion 
than the speed. The third kind of resistance as stated 
in (5) above is unimportant at low speeds, but may exceed 
the other two at high speeds. A longer ship may travel 
at a higher speed before the wave resistance begins its 
rapid growth than a shorter ship, but the skin resistance is 
greater. 

The stream line theory can be indicated most clearly by 
considering the immersed body held at rest with the frictionless 
heavy liquid of great extent passing by it. As the liquid opens 
out and closes in again in its passage its movements may be 
mapped out by a lattice of imaginary tubes filling the whole 
space, curved in form and varying in section in such manner 
that the liquid in moving through these tubes should move 
along the paths and at the speeds that relatively to the ship 
it actually follows. The forms of these tubes in any particular 
case may be observed by introducing streaks of coloured 
liquid. The tubes will in the neighbourhood of the stem 
and stern of a supposed ship-shape body be wider than at 
a great distance, and they will certainly be curved so that 
the convexity is towards the body. The tubes in the 
neighbourhood of the middle parts will certainly be narrower, 
for the space occupied by the body is not available, and 
they will also be curved with their concavity towards the 
body. Considering first the effect of curvature, the liquid 
in all the different tubes in being deflected from the straight 
course will exert a pressure normal to the tube on its concave 
side which will be felt outside on its convex side. Thus, 
near the stem and stern the surface of the body will experi¬ 
ence an excess of pressure which is the aggregate of that due to 
the liquid in all the imaginary tubes. Similarly, the middle 
parts will experience a corresponding diminution of pressure. 
Next, as regards the cross-section of the tubes, where the liquid 
is passing through a narrower portion it is flowing faster and 
its pressure is less, and conversely it is greater in wider portions. 
These changes of pressure in the liquid result simply from 
changes of its speed, and they are independent of the direction 
of motion. They depend upon the same hydro-dynamical 
principles that are made use of in the “ Venturi ” water meter. 


142 


DYNAMOMETERS 


The increase of pressure stem and stern and the diminution 
amidships, depending on the velocity of the liquid, must be 
added to the corresponding variations due to curvature of path 
in order to find the total increase at the ends of the body and 
diminution about its middle. It will be seen that these must 
be symmetrical and that the body is not subject to any force 
tending to make it follow the liquid. With a real liquid the 
only difference is the possible failure of the liquid to converge 
in true steam line motion and without eddies, and as the stern 
is made more abrupt the formation of eddies in the wake is 
made more pronounced. Whether the water moves past the 
body or the body moves through the water is immaterial, and 
so, except for the three kinds of resistance—skin friction, eddy 
friction and wave-making—there is no resistance due to 
movement through a liquid such as has been imagined and 
which may be considered as the pressure necessary to move 
the liquid out of the way acting over the immersed cross- 
section. The stream line theory shows that fine lines aft are 
the most important, and that a bluff bow has not the faults 
that would be anticipated. Nature has discovered this, and 
fish are a beautiful illustration. 

I may add a reference to an investigation of great importance 
by Prof. Osborne Reynolds published in the Phil. Trans. Royal 
Society, Yol. CLXXIV., 1884, pp. 935—982, and in Nature , 
Vol. XXVIII., 1883, pp. 627—632. In this research Prof. 
Osborne Reynolds investigated by the aid of colour streaks 
the conditions in which continuous or parallel flow of water 
changed almost suddenly to discontinuous flow with a different 
law of resistance. The velocity that could be reached before 
this condition occurred depended upon the viscosity divided 
by the density of the liquid, and as in the case of water this is 
double at 5° C. what it is at 45° C. the critical velocity 
admitted of considerable range. This speed also became greater 
as the diameter of the tube was larger. For velocities below 
the critical velocity the thin colour band passed along the tube 
its whole length as a clearly defined fine and the resistance was 
proportional to the velocity. When the critical velocity was 
reached the colour band almost suddenly formed whirls in the 
liquid and became uniformly diffused, but this never happened 
close to the entrance of the tube. The resistance then 


HISTORICAL 


143 


appeared to vary as the velocity raised to the 1*722 power, 
not to the square of the velocity. 

In the case of ships in air or water or aeroplanes speeds in 
which the surfaces in their passage would give rise to parallel 
flow, and hence to resistance proportional to velocity only, are 
too small to have any interest. Skin resistances at usual speeds 
follow a higher law than that of simple proportion.] 


CHAPTER X 


TRANSMISSION DYNAMOMETERS 

PAGE 

The function of this type of Dynamometer .... . . 144 

A. Morin : Translation from the French of his description of original dyna¬ 
mometers: Ernst’s integrator ........ 145 

Dynamometer of Messrs. Easton and Anderson ..... 161 

„ William Froude . . . . . . . .162 

,, Jervis-Smith.168 

Dynamic weighing by taring . . . . . . . . .171 

Dynamometer of Ayrton and Perry . . . . . . .173 

,, F. Von Hefner Alteneck ...... 174 

„ Matter. 174 

„ King.175 

„ [Boys].175 

„ Bourry.176 

„ Megy.176 

„ Ruddick.177 

,, Valet.177 

„ Neer.177 

„ Latchinoff ......... 178 

„ Tatham. .178 

„ Farcot. 179 

„ Parsons ......... 179 

„ Saurin.180 

» Dalby.180 

„ [Amsler].181 

„ [Moore].182 

[Worm-testing machine of Lanchester] ....... 184 

[Draw-bar dynamometers] . . . . . . . . .189 

Dynamometers of this type are placed between the prime- 
mover and the machine driven by it, and their function is to 
measure the power transmitted. Let it be supposed that the 
flywheel of a steam engine drives a dynamo, or any other 
machine, by means of a belt; then if we could make spring 
balances part of the belt, and the tensions of the tight and loose 
sides of the belt (often called the leading and trailing sides) 











TRANSMISSION DYNAMOMETERS 


145 


could be found and also the space through which the force 
acted, the work done would be known. Now, since this ideal 
condition cannot be realised, some machine must be employed 
capable of showing the difference of the tension of the 
leading and trailing sides of the belt, and also the distance 
through which this force has acted. Then the units of work 
expended during any instant equals the product of this 
force in pounds multiplied by the space in feet traversed in 
that instant. If by means of some mechanical process the 
differences of the tensions of the belt be continuously recorded 
and also the spaces traversed at each instant, during some 
known period of time, if the total time taken for any test be 
known, the data recorded afford a means of finding the average 
horse-power absorbed by the machine driven by the engine. 

In the history of power-measuring machines M. le General 
Arthur Morin * occupies the position of being the originator of 
dynamometric methods of measurements of peculiar and 
lasting excellence. He made his dynamometer self-registering, 
and exhibited the product of Force multiplied by the Space 
through which the force acted as an Area. He also invented 
and added to the dynamometer an integrator, by means of 
which the value of the area generated was found and the whole 
work done during any period of time estimated. As his work 
is so important, I here give nearly in full a free translation from 
the French of his description of his machines and instruments 
with exact copies of the original diagrams. 

General and 'particular conditions which dynamometers and 
apparatus destined to measure work developed by animate or 
inanimate sources of power should satisfy. —It has been already 
shown that the work developed by a constant force F which 
traversed a path E, with its point of application in the desired 
direction, was measured by the product FE ; if the force had 
been variable, the total work developed when it had traversed 
any path E would have been the sum of all the elementary 
quantities of work, such as Fe, successively developed through 
the elements e of the path traversed. In the last case it has 
been shown how, by the help of the calculus, or the method of 
quadrature of Simpson, the sum of products such as Fe has 
been found for the whole given path E traversed in the direction 

* “Notions Fundamentals de Mecanique,” A. Morin, Paris, 1855. 

L 


D. 


146 


DYNAMOMETERS 


in which the force acted. Finally the mean force of a variable 
one has been defined, and it has been shown how one may 
deduce the whole force by dividing the whole work by the whole 
path traversed. Apparatus destined to measure work developed 
by motors should indicate the product of the acting force and 
the path traversed, whatever their simultaneous variations 
may be. The illustrious Watt is the first who has satisfied the 
conditions mentioned in the construction of force measuring 
apparatus, to which he gave the name Indicator of Pressure. 
These are as follows :— 

(1) The sensitiveness of the apparatus should be propor¬ 
tioned to the intensity of the forces to be measured, and should 
not alter through the apparatus being used. 

(2) The indications of the bending of the spring should be 
obtained without calling for attention, or the inclination or 
bias of the observer, and should therefore be furnished by the 
apparatus itself, by means of traces, or material results which 
are left after an experiment is finished. 

(3) It is necessary that the force brought into play at each 
point of the space traversed by its point of application should 
be found, or in certain cases at each instant that the observation 
lasted. 

(4) If the experiment be extended over a long time, it is 
necessary that the apparatus should provide for the totalisation 
of the quantity of work given out by the motor (i.e., an engine 
of some kind). In order to satisfy condition (1) springs must 
be employed which bend in proportion to the forces acting, and 
which have the shape of bodies of equal resistance. This 
produces greater facility for recovery, and gives to the apparatus 
great sensitiveness. 

Rules for finding the proportions of the blades of a spring .— 
The theory of the resistance of material to bending, in agree¬ 
ment with the known results of experiment, shows that when a 
metal lamina of constant rectangular section is held in a recess 
by one of its ends the deflection varies directly as the load P 
and the cube of the length of the blade C, and inversely as the 
width of the blade A, the cube of the depth of the blade B, and 
the modulus of elasticity E. 

If the longitudinal profile (in depth) of the lamina is parabolic, 
for bodies of equal resistance the deflections under the same load 


TRANSMISSION DYNAMOMETERS 


147 


are double those which a lamina uniform throughout its length 
would give while its resistance to breaking remains the same. 

PC 3 

For springs of equal resistance we have F = a formula 


by the aid of which one is able to calculate any of the quantities 
which enter into it when the rest are known. Experience in 
the construction of a great number of laminae for springs has 
shown that when made of German steel of good quality, 
hardened and tempered to a suitable degree, the value of the 
coefficient of elasticity to be used was E = 20,859,000,000. 
This is estimated per square metre, it equals 2,085,900 kilo¬ 
grams per square centimetre, or 29,668,000 pounds per square 
inch (kilograms per square centimetre multiplied by 14-2262 = 
pounds per square inch). 

The relationship which it is convenient to establish between the 
different proportions of a spring. —The width a of the lamina 
should be limited to 4 or 5 centimetres at the most, because 
distortion caused by hardening is more marked as the lamina 
increases in size. It is this which introduces difficulties in 
adjustment. The observations made by me on springs have 
shown that the deflections of springs remain proportional to 
the applied forces, providing they do not exceed one-tenth of 
their length, for the strongest and one-ninth for the weakest, 
the measure being taken outside the fixed end. Accepting 
these data, it will be easy to calculate the thickness (depth) B 
which it will be suitable to give to a lamina at the fixed end, 
so that under a certain load it will take a known deflection. 
This dimension is given by the formula 


B 3 = 


PC 3 

EAF’ 


Longitudinal profile of the lamina of a spring. —The form of 
the longitudinal profile of the spring was deduced from the 

•g 

formula y = -^x, the values of B and C being those already 

given and the origin at the external end of the lamina. 

Arrangement of the blades of the springs. —The laminae of the 
springs used to measure the traction of carriages, ploughs, 
boats, etc., are shown in plan and elevation (Figs. 64 and 65). 
Two laminae, aa 1 , bb 1 , exactly similar, having their inner faces 

L 2 




148 


DYNAMOMETERS 



plane and their external ones parabolic, are terminated at their 
ends by connecting hinges of the same width as the laminae, 
bored with a hole. Small steel bolts fit these holes easily and 
engage with links //, to which they are fixed with nuts. The 


Fig. 65. 

























































































TRANSMISSION DYNAMOMETERS 


149 


lower shackle c was pierced with a recess to take the blade or 
lamina which was introduced lengthways ; a shoulder, of the 
length of the shackle, was fitted to the middle of the lamina 
and entered the recess exactly. Set screws g with conical points 
held the lamina in position. An external upper shackle d 
engaged the lamina aa and was furnished with a ring r, to 
which was attached the splinter bar or the rope on which the 
motor pulls. In order to measure large forces, four laminae 
were employed, the resistances of which united to balance the 
forces present. Deformation of the laminae was prevented by 
fixing in the shackle c two stops i joined by two crossbars e, 
against which the outer lamina came in contact when the 
tension exceeded its highest limit. 

Arrangement for obtaining a permanent trace of the deflections 
of the spring. —The front shackle carried a screw in a slot, by 
means of which a copper tube, terminated by a conical socket 
in which is fitted a quill pen, could slide and be retained by 
friction. The tube was filled with Chinese ink of suitable 
consistence. When the pen was well wetted and held correctly 
in its conical socket, capillarity sufficed to feed it constantly 
and regularly. The pen might be replaced by an ordinary 
lead pencil, or by one that does not require sharpening, but 
then a pressure of about 40 grammes would be required to 
make a sufficiently visible trace. The traces of the style were 
made on a band of paper coiled on a cylinder l , which served as 
a magazine ; the paper band passed over three small cylinders, 
which guided it under the styles and prevented its being bent 
by the wind or by its own weight. The band of paper was 
coiled on to another cylinder g, which acted as a receptacle for 
it and on to which one of its extremities was fixed with gum. 
A second style k, carried by one of the check pieces, and there¬ 
fore immovable, traced on the paper a line which corresponded 
to no force, or the position of the laminae when at rest, and it 
gave thus the zero of forces, so that the force acting is always 
measured by the displacement of the curve described by the 
moving style from the zero line. 

The method of moving the paper which received the trace of the 
style. —The motion of translation at right angles to the direction 
of the forces acting was transmitted to the band of paper by 
means of an endless cord which passed over the nave of one of 


150 


DYNAMOMETERS 


the wheels of the carriage and over a return pulley. On the 
prolongation of the axle of this pulley was an endless screw 
parallel to the laminse, which engaged with a pinion fixed on 
the axle of a small cylinder. On this was coiled a silk cord 
which transmitted the motion to the cylinder which received 
the paper band. By suitably proportioning this transmission 
gear with bands of paper 16 to 18 metres long, one could (using 
only one band) extend experiments over 800 to 1,000 metres 
or more. If the movement was transmitted directly to the 
axle of the receiving cylinder, the diameter of which was 
increased by the paper as it rolled on to it, the translation of 
the paper was accelerated. In order to prevent this incon¬ 
venience, the silk cord was coiled on a small intermediate 
cylinder fixed at its free end to a conical fusee having a screw 

A B 


l-1 



cut on its surface, its diameters being calculated, so as to 
compensate for the gradual increase of diameter of the receiving 
cylinder. 

Observations on the quadrature of curves traced. —From this 
description it is seen that the paper unrolls under the style 
with a speed which has a constant ratio to that with which 
the road was traversed; lengths of paper band represented the 
length of road on a scale known from the ratio. The ordinates 
of the curve of deflections measured from the zero line were 
proportional to the forces acting ; the result then was that 
the area included between the curve, the zero line, and any 
two ordinates, represented the total work done in that interval 
by the prime-mover. 

Methods of finding the quadrature. —Tedious methods are 
mentioned, and dismissed. The first method, which requires 
no calculation, consists in drawing a line AB (Fig. 66) 






TRANSMISSION DYNAMOMETERS 


151 


parallel to the zero line MN, at a given distance from it, 
greater than the maximum deflection, or equal to it. A con¬ 
stant fictitious force will correspond to that ordinate, to which 
will he due a known amount of work represented by the area 
of the rectangle MNB A. But abed ... NM was the real curve of 
forces given by experiment. The following ratios are therefore 
evident:— 

Area MNB A Work due to constant fictitious force 

Area abed ... NM — Work sought. 

Since the paper was machine-made of uniform thickness, 
so that the areas were to one another as their weights, by 
cutting them out and weighing the entire rectangle, and then 
the area bounded by the curve, the work could be found by 
simple proportion. Example:—When a 700-kilogram spring 
was used, T25 millimetre corresponded to a force of 10 kilo¬ 
grams, and a constant deflection, or a height of rectangle 
equal to 70 millimetres, corresponded to 560 kilograms. 
Calling P the weight of the band, 70 millimetres high, and p 
the weight of the part bounded by the curve and the zero 
line, E the length of the road traversed, F the mean force 
developed by the motor, we have 

F = 560 p kilograms, 

and the whole work done by the variable force will equal the 
product EF. 

Use of the planimeter .—The second method of obtaining the 
quadrature of the curve quickly without calculation is by the 
employment of the planimeter of Ernst (Figs. 67 and 68), 
which is furnished with a cone made of wood. This instrument 
consists of a cone beb, the axis of which is inclined with respect 
to the plane of the table which carried the instrument, so that 
(looking at a vertical section of the cone) its uppermost edge 
is parallel with this plane. The cone is carried on points by 
two supports fixed to the frame XX, and on the prolonged axle 
there is a small roller aa, which presses against a strip LL 
parallel to the guides, directed by which the frame XX moved. 
When the frame was pushed in either direction along LL, the 
roller and cone rotated and made a number of [turnsJ pro¬ 
portional to the path traversed by the frame. A counter, of 
which the most important organ is a, roller dd ,[having its plane 




152 


DYNAMOMETERS 


of rotation vertical and perpendicular to the upper horizontal 
edge of the cone, turning about an axis parallel to that same 




edge, is carried by a U-shaped bearing which forms a part of 
the transverse slide ff, which moves with the frame XX, and 
is also capable of motion in a direction at right angles to the 
strip LL, so that the roller can approach or recede from the 


Fig. 67. 
























































































TRANSMISSION DYNAMOMETERS 


153 


vertex of the cone as desired. The counter rests on the surface 
of the cone by virtue of its own weight, and when the cone 
revolves the roller does so also, and it is evident that the number 
of revolutions it makes is proportional (1) to the number of 
revolutions of the cone, or the length of the path passed over 
in the direction LL, and (2) to the distance of the roller from 
the vertex of the cone, or to the product of these two quantities. 
This being so, let us suppose that the roller was at the vertex 



of the cone. A point g on the slide ff corresponds to a line RS 
parallel to the guide LL : let it be on R ; it is evident that if 
the frame XX is pushed so that the point follows exactly the 
line RS, the roller will not rotate, since the velocity of the 
vertex of the cone is zero, but if the point g is on M, and the 
roller is distant from the vertex of the cone by a quantity 
equal to MR = NS, when the point is moved from M to N, 
the number of turns of the roller will be proportional to the 
length RS, which is the base of the rectangle MNSR and to 
the height of the same rectangle, and therefore to the area of 






























































154 


DYNAMOMETERS 


this rectangle. In the same way, if the point g follows the 
line OP, the number of turns of the roller will be proportional 
to the rectangle ORSP. In the construction of the instru¬ 
ment the roller need not reach the vertex of the cone, and 
therefore it is left out and the method of finding the area of the 
rectangle is slightly modified. Suppose, for example, one 
wishes to estimate the area of OMNP. The point g is brought 
on to the line MN, care being taken that it remains on the line 
during the traverse of the frame XX. The whole instrument 
is then pushed so that the point g passes from M to N. The 
roller of the counter makes a number of rotations proportional 
to the rectangle RMNS. The point g is then brought over P, 
then the frame is pushed backwards, so that the point g follows 
the line PO. During this retrograde motion the roller revolves 
in an opposite sense, and makes a number of turns proportional 
to the area of the rectangle ORSP, and since in these two 
consecutive movements it has rotated in opposite directions, 
it is evident that the final number of turns made is proportional 
to the difference of the two rectangles ORSP and MRSN, or 
to the rectangle OMNP. The movement of the roller is 
transmitted by gear to two pointers and dials, one of which 
shows units, tens, and hundreds of square millimetres, and the 
other thousands of square millimetres. What has been said 
about a rectangle applies also exactly to the quadrature of a 
bounded surface, such as those traced by the styles of dynamo¬ 
meters, bounded on one side by a straight line and on the other 
by an undulating curve op, since each element uvyx of that 
area may be regarded as a little rectangle of which the base 
is ux, and its height the arithmetical mean between uv and xy. 
In order to make the reduction of the curve or the quadrature 
of the area MNpo, one proceeds as follows. The sheet of 
paper is fixed under the table of the planimeter, so that the 
point g moves as near as possible to the table ; it follows 
accurately the line MN of zero force when the frame XX 
is pushed from M to N. Then the point g is brought on to M, 
the counter is lifted, and the two pointers set to their zeros ; 
the roller is gently placed on the cone, and the frame XX 
pushed so that the point g moves from M to N. The slide ff is 
moved so as to bring the point g on to p ; then by means 
of the compound movement imposed on it the point follows the 


TRANSMISSION DYNAMOMETERS 


155 


bends of the curve until it arrives at 0. The dials are then 
read, and they show the number of square millimetres con¬ 
tained in the area operated on ; dividing this number by the 
length of the base MN, measured in millimetres, the quotient 
gives the mean ordinate, or height of the rectangle equal to 
the same area, and therefore the mean force which has acted. 
In order that the operations described shall give an exact 
result it is necessary that in the motions either forwards or 
backwards the roller shall have no slip while revolving. This 
condition of not slipping is obtained by employing a cone of 
unpolished wood instead of the polished metal cone of ordinary 
planimeters. 

Dynamometer for totalising the work done during an interval of 
time or over a long road. —When the work done by motors during 
their passage over a long road 
is sought, the dynamometer 
furnished with the style and 
band of paper is inconvenient, 
and it is important that an 
apparatus which itself gives the 
total of the successive elements 
of work, so as to dispense with 
the quadrates described, should 
be employed. Such is the 
object of the following modi¬ 
fication introduced in the dyna¬ 
mometer mentioned in the 
preceding paragraphs. The 
back of the shackle is tra¬ 
versed by an axle rotating in it, on which is screwed a 
disc B (Fig. 69) having a diameter of 16 centimetres. Below 
the springs, on the axle of the disc, a pulley is fixed, which 
is rotated from the wheels by 



l i n 


i— 



ii* r 



d o 


L 








I \ - 

J 

Fig. 69. 


means of an endless cord 


passing round return pulleys. A column E, which forms a 
part of the shackle d, supports a counter which necessarily 
follows all the movements of deflection of the outer lamina 
of the spring. The important organ of the counter is a little 
roller carried on an axle parallel with the disc, its axis being 
in the line of traction. This roller acts in the same manner 
as that employed in the planimeter only ; since in place of a 



























156 


DYNAMOMETERS 


cone a disc is employed, the roller is able to reach the centre 
of this circle when the instrument is at rest. After what has 
been said respecting the planimeter it is not necessary to 
explain the action of this apparatus, and we know that the 
number of turns of the roller is proportional to the sum of the 
elementary products of the forces acting and the elements of 
the path traversed, or to the whole work done. The radial 
distance of the roller from the centre of the disc is reckoned in 
metres, under the strain due to the traction F, expressed in 
kilogrammes ; the radial distance is the deflection of the spring 
under this stress, providing that the apparatus is so arranged 
that the roller rests at the centre of the disc when there is no 
stress. Let 

r ± = radius of the roller ; 

e = the path traversed in one second by the carriage in the 
direction in which it is drawn, when the pull is 
constant, or in an infinitely small time, when the 
pull is variable ; 

R = the radius of the wheel whereby it is moved ; 
e 

n — = the number of turns of the wheel corresponding 


to the length of the path e ; 

F 

K = — — the relationship of forces to measured deflections ; 
r 

N = the number of turns of the roller for a path e ; 

R' = the radius of the nave of the wheel from which the 
movement of the disc is derived ; 
r' = the radius of the pulley of the disc. 


It is evident that the disc makes a number of revolutions 

— for one turn of the wheel, or for the path e 

r Z77xv r L 

traversed in the direction in which the carriage is pulled. The 

r 

roller will make - turns for one turn of the disc ; we shall 

r i 

e R' r 

have then N = ^ — for the number of turns of the roller 

Ztt Ja V T 2 

corresponding to a path traversed = e under a pull of traction 
F. The number N was moreover finite or infinitely small, 
provided that a constant force was dealt with, or a variable 


TRANSMISSION DYNAMOMETERS 


157 


force and an element of the path. We have by the definitions 


and Therefore 
or 


TZ F F 

K = - or r ==, 
r K’ 

N = 2^HrV,K Fe ' 

F«-"iN. 


Thus, either in the case of a constant force and a finite path, 
or a variable force and an elementary path, we see that the 
work developed by the motor is measured by the product of 

the constant factor and the number of turns N or the 

R 


elementary fraction of a turn made by the roller ; provided 
that the whole work at the end 
of any interval was the sum of 
elementary quantities successively 
developed, it will be equal to the 
same product by taking N equal 
to the turns of the roller during 
the observed interval. 

Apparatus of this kind has been 
employed with success and ease 
in prolonged experiments on the 
draught of carriages, and afforded 
means for determining the total 
work done by teams of horses six in number during a whole 
day’s work on the roads connecting Paris and Amiens and 
Nancy and Mans. 

Arrangement for indicating the number of turns made by the 
roller. —It is easy to see that the axle of the roller furnished 
with an endless screw (Fig. 70) may be made to communicate 
its motion by means of gear to two dials, one of which shows 
units and tens of turns, and the other hundreds and thousands 
of turns of the roller. In order to observe the divisions of the 
dials without stopping the apparatus or the progress of the 
carriage, two styles fed with thick ink are arranged so that 
they mark the enamelled dials when a button is pressed with 
the finger. Observations can thus be made and repeated 
without any confusion in the results. 

Chronomeiric motor dynamometer. —When experiments are 


























158 


DYNAMOMETERS 


required on the resistance of towing boats or vehicles without 
a forecarriage it is difficult, and in some cases impossible, to 
move the band of paper with a speed varying exactly as the 
path traversed. In this case it is much more convenient to 
employ a chronometric motor for giving the paper a sensibly 
uniform motion. Then lengths of paper generated in an 
experiment represent times, and the quadrature of the curve 
of deflections gives the sum of products such as F£, viz., of 
each force, by the elementary time of its duration, or that 
which we shall call, as will be seen later on, the total quantity 
of motion developed in the interval of time under consideration. 
By dividing the area found by the whole time, or by the length 
of the paper generated, we find the mean force of the motive 
power. In the haulage of ships, and in all cases in which 
speed would modify the results, two additional pencils are 
required ; of these one serves to mark points on the paper 
corresponding to equal intervals of time, viz., fifteen or thirty 
seconds, and the other distances traversed between posts or 
objects at a known distance apart. 

Rotational dynamometers .—The apparatus which has been 
described was constructed with a view to measure the power 
developed by motors, the direction of the action of which was 
in a straight line, or a circular path, but it has been easy to 
modify the machine so as to render it suitable for finding the 
work transmitted by a rotating shaft to any machine by 
employing the principle either of the styles or the counter. 

Description of the rotating dynamometer with the styles and 
paper recording apparatus. —On a shaft carried on two cast-iron 
columns (Figs. 71 and 72) three pulleys of equal diameter are 
placed ; of these A is fixed to the shaft, the other, C, next to 
the first, is an idle pulley, and the last, B, is movable on the 
shaft between limits which will be shown. This dynamometer 
was placed between the shaft of the motor (the engine) and the 
machine the resistance of which was sought. The idle pulley 
was embraced by a belt driven by the motor. When it was 
shifted on to the pulley A the shaft revolved, with a velocity 
which depended on the relationship between the diameter of 
this pulley and that of the pulley of the motor. The pulley B 
was furnished with a belt which transmitted the motion to 
the machine under trial and overcame its resistance ; but, 


TRANSMISSION DYNAMOMETERS 


]59 


since this pulley is loose on the shaft, it would not be carried 
round by the motion imparted to the shaft by the fixed pulley, 
unless a stop which forms a part of it were pressed by the end 
of the radial lamina of the spring which^is fixed in a boss. 
This lamina, turning with the boss, acts on a stop, the resistance 
of which causes it to bend, and when its resistance to bending 



Fig. 71. 


is sufficient to overcome that of the driven machine, motion 
begins, and is transmitted to the shaft of the machine under 
trial, by the intermediary spring, the deflections of which are a 
measure of the resistance to be overcome. A style attached 
to one of the spokes of the pulley touches a band of paper 
moving at a speed proportional to the speed of the shaft, and 
on it it traces a curve of deflections in just the same way as in 
the dynamometers used in testing carriages. Another style, 
which however is fixed, traces at the same time a line 












































160 


DYNAMOMETERS 


corresponding to no deflection, or the position which the 
moving style occupies when the force is zero. This zero line 
is found about the middle of the width of the paper band, so 
that the force can be measured indifferently in one sense or 
the reverse. The laminae are of parabolic section, and one can 



employ as many as one wishes, according to the intensity of the 
forces which the apparatus is required to measure. A fixed 
stop on the shaft limits the displacement of the pulley, and 
therefore the deflection of the spring; this prevents over¬ 
loading in case of accidents. 

The transmission of motion of the shaft to the hand of paper ,— 
A collar provided with helicoidal teeth rides loose on the 
shaft; its teeth engage with a pinion the axle of which (viewed 











































TRANSMISSION DYNAMOMETERS 


161 


in a plan perpendicular to that of the shaft) does not meet this. 
The axle of this pinion is furnished with an endless screw, 
which engages with another pinion carried on the prolongation 
of the axle of the small cylinder on which the silk cord is coiled 
which moves the fusee. To start the band of paper the toothed 
collar is stopped by means of a clutch, against which a stop 
projecting from the collar comes in contact. Then when the 
toothed collar is fixed in space, so that the pinion carried by 
the shaft rolls over it, this pinion receives a relative motion 
which it transmits to the screw, the fusee, and the band of 
paper. 

In apparatus of this kind a conical fusee serves to regulate 
the movement of the bobbin which carries the paper ; by the 
introduction of this intermediate organ the growth of the 
diameter of the paper on the receiving cylinder is compensated 
for, as has been already shown. 

The rod which moved the roller of the integrator also 
actuated a tracing point, which marked a curve on a band of 
paper moving at a rate proportional to belt speed. The 
mean force acting was found from the area of the curve, and 
also the whole Work done. In a dynamometer built for the 
delivery of 50 horse-power the springs were six in number, 
made of steel of flat-tapered shape, fixed to the central boss, 
and bearing on rollers at their outer ends. That Morin should 
have designed an original form of dynamometer automatically 
recording the product of two quantities, which has been the 
model of several similar machines, which have been employed 
in very important official tests of competing machines, bears 
circumstantial testimony to his ability as an engineer. 

Dynamometer by Easton and Anderson. 

In a later form of this type of dynamometer made by Messrs. 
Easton and Anderson, of Erith,* curved springs were employed 
instead of straight ones, the curvatures being placed in opposite 
directions so that the effect of centrifugal force on the 
springs was minimised. The boss of the wheel, which was 
displaced by the deformation of the springs, was furnished 

* Proceedings of the Institution of Mechanical Engineers, 1876 ; see ibid., 
p. 199, W. E. Rich. 

D. 


M 


162 


DYNAMOMETERS 


with a coarse-pitched double-thread screw which was in contact 
with a little cross-head, which passed through a slot in the shaft. 
The cross-head was free to move along the axis of the shaft in 
line with it. A rod attached to this cross-head projected from 
the shaft, and was connected to an integrating apparatus, of 
the disc and roller kind, described under the heading 
44 Integrators.” 

The Transmission Dynamometer of William Froupe. 

To understand fully how belt dynamometers act several 
points must be observed. The belt, in order that it may 
adhere to the pulleys driven by it, must possess sufficient 
initial tension to prevent slipping. If no friction existed in 
the machine and it was in motion, this tension would be exactly 
the same, on the leading and trailing sides of the belt. If the 
machine opposes motion from both friction and imposed load, 
then the belt will’be in greater tension on the leading side than 
on the trailing one ; the difference of these tensions on the 
two sides of the belt enable motion to continue against the 
imposed load ; so if this difference of tensions be known, the 
power transmitted can be at once determined, in the same 
manner as if fhe motion of the pulley were due to a force equal 
to this difference of tensions acting at its circumference. 

“ Hence the power consumed, or the units of work expended during 
any instant, will be the product of the difference in pounds between the 
tensions of the leading and trailing sides of the belt at that instant 
multiplied by the space in feet travelled by the belt in that instant.” 

The recording apparatus used in connection with this 
machine gives the sum of all such elements of work, and 
therefore the whole work done, during any certain period of 
time. The figures (73 and 74) show the machine in side and 
end elevation. The power is supplied by the pulley A and 
consumed by the pulley B, which drives the machine to be 
tested. The direction of motion is shown by the arrows. The 
belt conveying the power passes over the pulleys CD, the 
axles of which are carried on the opposite ends of the beam E 
at equal distances from the point about which it is free to 
vibrate. The upper and lower portions of the belt are kept 


TRANSMISSION DYNAMOMETERS 


163 



parallel, even when the beam is displaced through several 
degrees from the vertical, by means of the guide wheel G. 
The leading side of the belt passes round the pulley C on the 

M 2 


































164 


DYNAMOMETERS 



beam, and the trailing side round the pulley D ; thus the 
pulley C is pressed horizontally by the tight side of the belt. 
The pulleys C and D are carried on axles which bear against 
antifriction rollers NN (Eigs. 73—77). 















































































TRANSMISSION DYNAMOMETERS 


165 


“ If the tensions of the two parts of the belt were equal, then the 
beam would remain in equilibrium, but since they are not equal, the 
spring balance I receives the resulting pressure of their inequality, and 
indicates its amount by its extension. The pressure is an exact measure 
of the difference of tension before mentioned. Now these tensions, 
which vary with the force at any instant absorbed by the machine under 
test, are continuously recorded on a band of paper travelling at a rate 
proportional to the belt speed ; so that the area of the curve recorded, 
on integration, gives the whole work done in any set time. It must be 
noticed that the total tension on each of the pulleys carried by the 
beam is double that of the respective portions of the belt, since the 
tension of the belt acts on each side of the pulley; thus the spring 
balance indicates twice the difference of the tensions of the leading and 
trailing sides of the belt. Due allowance is made for this in the for¬ 
mation of the scale of force on the record traced on the cylinder. The 
speed of the recording cylinder is proportional to the belt speed, and 
represents it on a reduced scale. 

“ A pencil, deriving its motion from the beam E (Fig. 75), marks the 
extension of the spring balance on the moving cylinder. Since in this 
type of machine the spring balance has a tendency to oscillate on either 
side of its mean position, this motion is checked by the introduction of 
an oil dash-pot, that is, a cylinder having a loosely-fitting piston attached 
to the spring balance ; the ends of the oil cylinder are connected by 
means of a tube, through which the oil can flow when conveniently 
checked by a stop-cock. The recording cylinder is provided with a 
continuous sheet of paper, which is uncoiled from a lower cylinder; 
and as it revolves the pencil tracas on the paper a line, or rather a 
curvilinear area, in which each increment in length represents the 
corresponding space travelled by the belt, while the height of the point 
measured from the datum line traced by the pencil, when the spring 
balance is at zero, represents the stress upon the spring balance while 
the belt travelled through that space. The aggregate area included in 
an} length of the diagram thus produced represents, therefore, exactly 
the units of work performed in that time ; this is easily measured in 
the same manner as an indicator diagram, and can then be converted 
into units of work performed, when the scale by whicn the conversion 
is to be effected is determined.” 

In these tests the driving band is replaced by a continuous 
cord (mentioned in the introduction) running over grooved 
pulleys, these grooved pulleys corresponding to the belt pulleys 
of the transmission dynamometer described. In order that the 
pulleys might be relieved of friction, they were carried on a bent 


166 


DYNAMOMETERS 


bracket (Figs. 76 and 77) furnished with a friction roller N on 
each side. And to avoid any oblique deflection the arms of 
the swing balance were cranked (Fig. 74). This produced a 
corrective couple, and the axes of the pulleys were kept truly 


Tension 

Lbs 



\y\A 

J\AM 

fwvX 



t 1 

l, 

4 l 

i, 

i 


- 9 * --U--U--U-U-u--(1- 

O JOO ZOO 300 400 „ , 5QO 

tuM&uilums 


Fig. 78. 


parallel to the axis of the beam. The leading side of the belt 
(Fig. 73) runs on the upper pulley C, and opposite, and on a 
level with it, the indicating apparatus K is placed. The belt 
used in this machine consisted of a double thickness of strong 


m - 

1 


HIaM/ 


ioo\ - 

Mat/un&cnydA 

gw 

MV 

il “ n 


50 ^VNfYrvV 

—o -- \ 

I 

X— i —, 

A 

J_ 1 _ 


Fig. 79. 


webbing sewed together and saturated with boiled oil. Such 
a belt proved itself to be remarkably supple, smooth, tenacious, 
and adhesive. Diagrams taken from trials are shown in the 
figures (78—80), which are portions of the actual traces made 
by the indicator pencil. The horizontal lines indicate tensions 
























TRANSMISSION DYNAMOMETERS 


167 


of 50, 100, and 150 lb.; while the vertical lines are marked in 
intervals of 100 revolutions of the pulley on the beam. In 
Fig. 78 the diagram of power expended in thrashing barley is 
shown, the total mean tension being 85 lb. ; Fig. 79 is another, 
for thrashing wheat, total mean tension 110 lb. ; Fig. 80 is a 
diagram of chaff-cutting. 



The following summary gives the relative value of work done 
in thrashing in each case 

Number of sheaves thrashed 
Mean tension of belt (pounds) . 

Total number of revolutions 
Total length of belt passed (feet). 

Total units of power consumed 
(foot-pounds) 

Units of power consumed to 
thrash one sheaf (foot-pounds) 

Total time occupied in thrashing 
200 sheaves (minutes) . 

Horse power for driving thrashing 
machine in work . 


Horse power = Total time 


X 


Wheat. 

Barley. 

200 

200 

110 

85 

7,525 

7,050 

23,636 

22,148 

2,600,290 

1,882,580 

13,001 

9,413 

11-40 

10-68 

6-914 

5-343 

Lds. _ „ _ 

Or foot-pounds per 


minute divided by Watts’s constant of 33,000. 

This description of the dynamometer of William Froude is 
practically an abstract of a paper in the Proceedings of the 
Institution of Mechanical Engineers, July 28, 1858, and I 












168 


DYNAMOMETERS 


have to thank that institution for permission to reproduce the 
figures. 

The recording cylinder K is driven from the pulley C by 
means of two successive worm wheels R and S (Figs. 74, 75), and 
the speed is thus reduced to -g-^Vo the P u Uey. The 

first wheel R is furnished with a cam, which moves another 
pencil close to the indicating pencil; this when unmoved by 
the cam traces a straight line along the paper, but at each 
revolution of the wheel the cam makes a narrow mark on this 
line, the length between the marks equalling 157 feet of belt. 

Calibration of the diagrams .—The working belt is removed, 
and another belt is fixed to the point 0 in the frame. It 
passes over the power pulley, then round the pulley C, and over 
the guide pulley G. To the loose end of this belt weights 
are suspended. For determining any scale a weight sus¬ 
pended from the end of the belt gives the same stress on the 
spring as an effective driving force of the same amount. If 
now the paper is moved a little by hand, the position of the 
pencil for the load is marked on it. The reading of a diagram 
is greatly facilitated by causing eight pencils to rule lines along 
the diagram at distances from the base line showing different 
loads. It is also found convenient to rule lines of different 
colours which denote the different loads. Such coloured lines 
are now used in dynamometer diagrams produced in the tests 
of ship models. 

I have given a full description of the dynamometer of 
William Froude in the first place because it is very clear and 
definite, and secondly because the method employed for 
obtaining a record of the measurement of the power trans¬ 
mitted is practically the same as that now used in the ship- 
model testing department of the Admiralty, and also naval 
departments of other nations who have followed the example 
of the British naval authorities. 


Transmission Dynamometer by the author, Philosophical 
Magazine, Vol. XV., p. 87 ; and “ Dynamo Electric 
Machinery,” by Professor S. P. Thompson, 1884, p. 383. 

A steel shaft, tubular at each end (Fig. 81), and opened out 


TRANSMISSION DYNAMOMETERS 


169 


into a wide slot between the pulleys and one of the bearings, 
carries two pulleys, one keyed to the shaft and provided with 
two bevel wheels, the axes of which are in the plane of rotation 


Band Band to 



Section at A A. 



of the pulley ; to the other a concentric bevel wheel is fixed, 
which engages with the two former ones. If the loose pulley 
is displaced with respect to the fixed one, the two bevel wheels 
are rotated, and by their rotation through connecting bands 






























































89 


170 


DYNAMOMETERS 


attached to cylinders which form a part of each they extend 
spiral spring the axis of which lies in the axis of the shaft, 
rod attached to a cross-head which moves in the slot before 




mentioned (Fig. 82), which is attached to the spiral spring 
and moves with it as it is extended, passes through the tubular 
end of the shaft, and to it is connected an integrating apparatus 
(described in the chapter on “ Integrators ”) which records the 




















































































TRANSMISSION DYNAMOMETERS 


171 


power transmitted by the machine when driven by an engine 
and driving a machine to be tested for consumption of power. 
The same rod moves a pencil over a recording cylinder (Figs. 
83 and 84) similar to that used in the dynamometer of 
W. Froude. The spiral spring was placed where shown in 
order to minimise the action of centrifugal force on it. In 
my later machines of this type, the cross-head is connected 
to the bevel wheels in such a manner that the flexible connection 
does not introduce any deformation due to centrifugal force 
which might interfere with the equilibrium of the system. 
Sometimes when the machine is driven by a turbine or motor 
at a uniform speed the force acting is shown immediately 
on a dial. The dynamometer was calibrated by the same 
method as that employed by W. Froude already described. 

The author also employed another method of calibration, 
described in “ Work-Measuring Machines ” (Messrs. E. and F. 
N. Spon, 1884). It is as follows :— 

“ Lot a prime-mover (a water-wheel appears to be most steady) 
drive the transmission ergometer, and let the ergometer drive a pulley 
on a shaft embraced by a Pronv or other suitable friction ergometer, 
and let the work done against friction be calculated. This should 
agree with the results of the transmission machine. If it does we may 
conclude that it has been correctly calibrated. The advantage of this 
method is that the transmission machine is tested while running in its 
usual condition.” 

I have called this process of calibrating Dynamic Weighing 
by Taring. 


Dynamic Weighing by Taring. 

The method of weighing by taring, due to Borda, employed 
when the ordinary balance is used to determine the weight of 
any object is to place the object in one pan of the balance 
and then counterpoise it with any convenient material, such as 
shot and sand, placed in the other pan. The object is then 
removed and replaced with known weights which exactly 
equilibrate the counterpoise ; then the sum of the known 
weights equals that of the object weighed. The advantage 
of the method is that error due to lack of equality in 
ength of the arms of the balance is not introduced. 


172 


DYNAMOMETERS 


As an extension of this method, which may be shortly stated 
as making both A and B equal to C, and consequently equal 
to one another, I devised the following method of comparing 
the work done in driving any machine, such as a dynamo or 
screw propeller, with a definitely known amount of work done, 
under exactly the same circumstances, by the same prime - 
mover. An example of the application of the method may be 
considered. We wish to compare the power absorbed by a 
given machine such as a propeller with the power absorbed 
by a rope brake. An electric motor is attached to the pro¬ 
peller and the exact readings taken of the watts consumed 
during the run. Then the propeller is detached and replaced 
by a rope brake dynamometer. The former electrical readings 
are re-established and the brake horse power determined from 
the rope brake dynamometer. Then this brake horse power 
equals that absorbed by the propeller. 

This method has shown itself by no means difficult to carry 
out; and when the electrical instruments are close reading, 
and dead beat, there is no reason to suspect it of error. The 
current is best read by reading the potential difference at the 
extremities of a known resistance in the supply circuit. The 
supply should be taken from accumulators so that the E.M.F. 
may be constant. It is nearly impossible to obtain a really 
constant E.M.F. from an ordinary town supply of electricity. 
The method suggested itself to me while testing a transmission 
dynamometer against a brake dynamometer. To make the 
method generally useful in the mechanical laboratory it was 
found necessary in some cases to alter the speed of the driving 
shaft. It is not a difficult matter to regulate the apparatus so 
that the speed of rotation may be the same in each case. 

For reading the speed of the shaft either the optical methods 
of Lord Rayleigh * or Mr. Bosanquet are suitable. In the 
apparatus of Mr. Bosanquet a disc perforated with radial slots 
rotates on the shaft, and a tuning-fork, driven electrically, 
vibrates at right angles to the radial slots, close to the disc. 
When the combined motion is viewed by looking through the 
slots, and the number of slots passing per second equals the 
number of vibrations of the fork, a fixed wave line is visible, but 
if these numbers are not equal, the wave line shifts to the right 
* Proc. Royal. Soc., 1881, p. 111. 


TRANSMISSION DYNAMOMETERS 


173 


or left, showing that the speed has either increased or decreased. 
This method is exceedingly accurate, and, though perhaps 
rather too physical in its nature to commend itself to the 
engineer, would well repay the experimenter for trouble 
expended on it. In the case of ordinary speed indicators we 
have to take them on trust, as correctly calibrated, and assume 
that their accuracy has been preserved, after daily use. In the 
optical method we have to rely on the time-keeping qualities 
of the tuning-fork. Experience extending over many years 
has shown that a well-made standard fork, such as those of 
Koenig, maintain their accuracy of vibration for very long 
periods, if preserved from any rust and injury. By employing 
a counter such as that of Harding and a well-rated stop-watch, 
the total revolutions during any set time may be found, but 
this method does not show any variations on either side of the 
mean speed ; the optical method, however, does show these 
variations in a very marked manner. 

Transmission Dynamometer by Ayrton and Perry.* 

In this dynamometer the two halves of a flange are connected 
by means of spiral springs, and when the shaft to which the 
half-flanges are fixed transmits power they are extended. The 
extension of the springs is shown by means of a bright bead 
attached to the end of an arm which is moved towards the axis. 
The background over which the bead moves is dead black. 
When the shaft rotates the bead describes a luminous circle, 
the radius depending on the extension of the springs. A scale 
having a sliding pointer enables its position to be read. The 
reading on the scale multiplied by the number of rotations per 
minute of the shaft gives at once the horse power actually 
passing through the coupling. The same principle is also 
embodied in a transmission dynamometer which can be moved, 
so as to test any fixed machine. In this apparatus the reading 
is made in the same manner as in the former one described, 
but the shaft is provided with three pulleys, two of which 
belong to the dynamometer proper, while the third is an idle 
pulley, on which the driving belt runs when the machine is 
not in action. 

* “Applied Mechanics,” by John Perry, F.R.S., Cassell & Co., 1897. 


174 


DYNAMOMETERS 


The Transmission Dynamometer of F. yon Hefner 
Alteneck. * 

In this apparatus a continuous driving band connects the 
engine with the machine under trial. About midway between 
the two pulleys a balanced frame carries two guide pulleys, 
both of which are in contact with the outside of the driving 
band. The distance between them is such that the band is 
constricted by passing between them. When the angle made 
by the following side of the band on either side of the guide 
pulley equals that made by the leading side on either side of 
its guide pulley, then a certain force is required to keep the 
frame and guide pulleys in a symmetrical position. This force 
was measured by a spring which was extended by means of a 
screw, until an index reached its normal position. The force 
thus found, divided by the sum of the sines of the two angles 
made with the centre line by the two parts of the driving 
band on each side of the same guide pulley, equalled the 
difference between the tensions of the leading and the trailing 
sides of the band. In another form of this dynamometer, in 
order to simplify the reading of the angles involved, the band 
was led over seven pulleys carried on a frame capable of dis¬ 
placement. To check vibration a small dash-pot was con¬ 
nected to the frame. No account is given of the friction 
which would arise from employing so many pulleys. One 
would imagine that it would out-balance the small inaccuracy 
due to determining the angle between the sides of the band 
and the central line. This machine did good service when 
.used to find the efficiencies of dynamo-electric machines. 


The Dynamometer of M. Matter (used by MM. Dolfus Mieg, 
of Mulhouse). 

The interesting feature of this machine is the introduction 
of a power diagram, on which curves are traced which are the 
loci of points for which the product of effort multiplied by 
speed are constant. This is evidently the rectangular hyper¬ 
bola. The power diagram is generated and used thus. The 

* “ Seprat-Abdruck aus den Bayerischen Industrie und Gewerbeblatt,” 1883, 
heft 1. 


TRANSMISSION DYNAMOMETERS 


175 


abscissae are proportional to the velocity in metres or feet per 
second, and the ordinates to the force in kilograms or pounds. 
The loci of all points for which the product of these factors 
equals a constant lie on a curve of equal powers. Several such 
curves are carefully drawn on a surface so actuated by the 
dynamometer that displacement along the line of abscissae is 
proportional to speed (this is effected by a speed indicator of the 
Buss type) ; at the same time the surface is moved at right 
angles to this direction by the machine, so that the ordinates 
are proportional to the force at any instant. The position of a 
stationary point in front of the diagram will be situated on, or 
near, a curve which at once shows the power transmitted by the 
dynamometer. For example :—Let equal distances along the 

line of abscissae denote 1, 2, 3,.metres per second, and 

the ordinates 10, 20, 30,.kilograms, then, where a line, 

for instance, through 7*5 metres per second, cuts a line through 
10 kilograms, we find a point on the curve such that their 
product equals 75 kilogram-metres, or one force de cheval , or 
French horse-power. 

The Dynamometer of King. 

In a dynamometer by King, which is quite unique, a spring 
of horse-shoe shape is placed actually in the driving belt con¬ 
necting its ends ; as this travelled with the belt it registered 
the tension by means of a pawl and ratchet wheel, the reading 
during a given time being that of alternate tensions. The 
original account of this apparatus is brief. 

[The Dynamometer of C. V. Boys.] 

[A transmission dynamometer described by C. V. Boys at a 
lecture at the Royal Institution * depends on the fact that if 
the driving belt is elastic, as for instance is the case with belts 
made of a close helix of steel wire, the spires are somewhat 
more open in the tight side than they are in the loose side. As 
the belt does not accumulate at one pulley, the linear velocity 
of the tight side must be greater than that of the loose side 
to such an extent that the same number of spires pass any 
point in a given time on the two sides. The tight side passes 

* Proceedings of the Royal Institution, 1883, page 241. 




176 


DYNAMOMETERS 


on to the driving pulley, which accordingly moves at the speed 
of the tight side, while the loose side leads on to the driven 
pulley, which in the same way travels at the speed of the 
loose side. The driving pulley therefore turns somewhat more 
quickly than the driven pulley if they are of the same diameter, 
the difference being proportional to the driving couple. In 
order to record the difference in speed a crossed band from a 
pulley on the driving shaft was made to turn an equal pulley 
riding loose on the driven shaft at its own speed in the opposite 
direction. A differential gear connecting the two pulleys on 
the driven shaft then moved with a speed proportional to the 
rate at which work was being transmitted, for this speed is the 
product of the speed and the difference of speed or torque. 
Thus it automatically integrates the work transmitted, and 
time records of this give the average power in the intervals. 
This is not suited in the form described for measuring more than 
small power, but the same author has shown how by an 
epicyclic connection any known small fraction of the torque 
may be transferred from one shaft to the other by an elastic 
band, the rest being transferred by a nearly inelastic belt, 
such as the usual leather belt, or absolutely.] 

The Dynamometer of M. Bourry. 

In this machine the angular displacement of two pulleys 
by means of bell-crank levers compresses springs. The motion 
of compression acts on a disc which slides on the axle and 
actuates the integrating apparatus. The machine is furnished 
with a lever connected with the disc mentioned, designed to 
regulate the speed of the engine driving it; so that it became 
a dynamometric governor. 

The Dynamometer of M. Megy. 

This machine, which was made by the firm of Sautter 
Lemonner, of Paris, consists of a horizontal axis carried on 
two bearings, beyond one of which it projected. To the pro¬ 
jecting end a pulley was keyed. On the inner side of this 
bearing a loose pulley was placed ; a boss, bearing against the 
nave of the loose pulley and fixed to the shaft, carried two flat 
steel springs similar to those by Morin ; these were in contact 


TRANSMISSION DYNAMOMETERS 


177 


with the loose pulley near its face. An elongation of this boss 
which carried the springs was screwed with a quick pitched 
thread, which engaged with a nut which was rotated by means 
of two studs projecting from the loose wheel. When the 
loose wheel was displaced with respect to the fixed one the 
springs were deflected and the nut rotated, which caused it to 
traverse the shaft lengthwise. The motion was transmitted 
to the recording integrator of the disc and roller type. This 
machine did excellent service in the early days of testing 
dynamo-electric machinery. 

The Dynamometer of Rtjddick. 

In this machine the parts which are displaced are fixed 
directly on the shaft. In several ways its action is similar to 
that of the Ayrton and Perry flange dynamometer. The dis¬ 
placement of a pulley with respect to a flange compresses 
springs, and the displacement is magnified by means of a lever 
carrying a pencil at its end, which marks a disc carried on the 
shaft. The pencil approaches the centre of the disc as the 
force transmitted increases. The disc* is rotated by means of 
a ratchet mechanism moved at each rotation of the pulley. 

The Dynamometer of Yalet. 

In the dynamometer of M. Valet the displacement of a 
pulley with respect to a shaft is shown by a recording appa¬ 
ratus, the springs in this machine being of the flat type. The 
recording apparatus rides on the shaft, and is prevented from 
rotating by a projection. 

The Dynamometer of Neer. 

In this machine the two halves of a flange coupling are 
connected to one another by means of four rollers placed at 
equal distances on the face of one flange, with their axes at 
right angles to it. Over these four link chains pass, one end 
of each being fixed to the other flange, and the other end of 
each chain being attached to a sleeve capable of movement 
along the shaft, and in so doing compressing eight spiral 
springs. The motion of the sleeve is very closely proportional 


178 


DYNAMOMETERS 


to the couple existing at any moment between the flanges. 
This and also the revolutions are shown on two dials. 

The Dynamometer of M. Latchinoff. 

Two pulleys are connected by means of spiral springs, and 
the displacement is read by utilising the phenomenon of the 
persistence of vision. One pulley is marked on the inner side 
of the face with divisions and the other with a single mark. 
The position of this mark on the curved scale is viewed through 
a slot in the face of the pulley, so that an image of its position 
is seen for an instant at each revolution. Although this dyna¬ 
mometer is not well known, it embodies a very interesting 
physical principle, which is bearing good fruit at the present 
time in connection with at least three forms of Torsion meters. 

The Dynamometer of Tatham. 

This machine in certain respects resembles the belt dynamo¬ 
meter of W. Froude. It consists of six pulleys, two of which are 
carried at equal distances from the fulcrum of a lever or frame 
free to move about a knife edge. Two are carried on bearings 
in the same vertical line, below those on the lever ; each of 
these is on a shaft furnished with a pulley, one of which is 
driven by the prime-mover, while the other drives the machine 
under test. A continuous band passes round the four former 
pulleys, and the difference of tension in the band deflects the 
lever, to the end of which a steelyard type of balance is 
attached. The fulcrum of the balance can be adjusted so that 
it may be kept horizontal under the load to which it may be 
subjected. In the machine of W. Froude it will be remembered 
that careful provision was made for keeping the sides of the 
band parallel, so that changes in the angular position of the 
beam would not affect the effective working of the machine. At 
the same time it afforded a means of obtaining an automatic 
record of the power employed. In another dynamometer by 
Tatham, in place of the two pulleys carried on the single beam, 
two beams or levers are employed, and by each a pulley is 
carried. Each of these beams or frames is supported at their 
external ends on knife edges and planes, and their inner ends 
are connected by links to a weighing beam placed above them, 


TRANSMISSION DYNAMOMETERS 


179 


so that the difference of tension on the two pulleys can be 
found. In this machine the leading and trailing sides of the 
belt are parallel. It will be noticed that this condition is 
practically obtained by carrying the two upper pulleys on two 
beams which are free to move on pivots ; at the same time 
provision is made for giving to the band sufficient initial 
tension for driving purposes. The band used in this machine 
was of leather, the joints being carefully and smoothly made. 
The flesh side was next to the driving pulleys and beam pulleys, 
and the hair side next to the upper central pulley. If a belt 
is fairly long, and narrow, one of its surfaces can always be 
used in contact with three pulleys. All that has to be done is 
to give the belt a half-turn on either side of the intermediate 
pulley, then the same side of the belt will touch all the pulleys. 
[A belt with a half twist in it is specially suitable for driving 
between pulleys on shafts which make a large angle with one 
another. Such a form of belt is well known as having one 
surface and one edge only.] 

The Dynamometer of M. Earcot. 

The principle underlying the mode of action of this machine 
is practically that of both Froude and Tatham. The sides of 
the belt are kept approximately parallel and two tension 
pulleys carried on separate levers or frames placed under 
the driving pulley instead of above it, as in the dynamometer 
of Tatham. 

The Dynamometer of Parsons. 

In a dynamometer of Parsons* the same idea is found. 
Vertically below a grooved driving pulley the driven pulley is 
placed. A continuous rope passes over the driving wheel, then 
round a pulley in a block from which a weight hangs, then 
round the driven pulley, and then round a pulley in a block 
back to the driven pulley. The difference of the tensions of 
the two sides of the rope is found by taking the difference of 
the values of the suspended weights required to establish 
equilibrium when the machine is running. This dynamometer 
was used by its inventor in connection with experiments on 
screw propellers. 

* Proceedings of the Institution of Mechanical Engineers, 1877, Hon. R. G. 
Parsons. 

N 2 


180 


DYNAMOMETERS 


The Marine Dynamometer of Saurin. 

In this machine, which is amongst the earliest employed for 
measuring the output of a marine engine, the springs, which 
are deflected by the imposed couple, are of peculiar shape. 
Mr. Gisbert Kapp, in his excellent articles on “ Dynamo¬ 
meters ” in The Electrician of January 19th, 1884, makes the 
following remarks on this dynamometer, which he attributes 
to M. Saurin (in La Lumiere Electrique the name is spelt 
k < Taurines ”) :— 

“ If a straight spring of uniform section he held rigidly at one end, 
and the deflecting force applied at its free end in a direction perpen¬ 
dicular to its length (similar to the load on a cantilever), then a minimum 
of force will produce a maximum deflection. If both ends are supported 
and the load applied in the middle, the deflection will be only one- 
quarter of what it was before. Or, for the same weight of steel employed 
and with an equal deflection, the force to be measured can he quad¬ 
rupled. This arrangement will, therefore, be better than M. Morin’s 
original plan of straight radial springs, if large powers are to be trans¬ 
mitted. But M. Saurin goes a step farther. He employs springs 
slightly curved, and applies the power in such direction as to pull the 
ends apart and thus straighten the springs. With this arrangement a 
minimum weight of steel can register a maximum pull at a moderate 
deflection, as indicated by the more or less complete straightening of 
the bent springs. The propeller shaft is divided and connected by 
means of an elastic coupling, consisting of two cross-bars and two 
curved springs. One cross-bar is on the engine side of the shaft, the 
other on the propeller side. Studs project from the ends of these 
cross-bars, which engage with the ends of the curved springs. The 
springs are placed with their convex sides outwards from the shaft. 
The effect of a separation of the ends of the cross-bars is to pull the 
springs out and make them straight. The resistance to straightening 
is obviously very great, and this form of spring apparently provides 
the condition of minimum weight for maximum transmission of energy. 
The displacement of the springs makes an automatic record of force 
while a fixed pencil draws a datum line from which to reckon the value 
of ordinates.” 


The Dynamometer of Professor Dalby. 

A pulley drives a shaft through a spiral spring. The dis¬ 
placement of the pulley with respect to the shaft is indicated 


TRANSMISSION DYNAMOMETERS 


181 


by means of a very interesting mechanism. Two equal 
sprocket wheels are attached, the one to the spring pulley, the 
other to the shaft. An endless band of steel passing over them 
forms two loops, which remain at the same distance apart 
when the system is rotating, but if angular displacement takes 
place between the two sprocket wheels their distance is changed, 
and this change is proportional to the torque transmitted by 
the shaft. In order to measure this, two guide pulleys are 
placed in the loops, guided by a geometric slide. One of these 
pulleys carries the scale and the other an index. A reading 
on the index is proportional to the torque. Should oscillations 
occur they may be damped by the introduction of a dash-pot, 
or, which is better, practically prevented by employing a 
relatively stiff spring. 

[The Dynamometer of Amsler.] 

[The transmission dynamometers of Dr. Alfred Amsler wer« 
shown at the meeting of the Institution of Mechanical Engineers 
held in Zurich on July 25, 1911, and an illustrated account of 
them is given in the Proceedings of that Society for that date, 
pp. 603—616. I am indebted to the courtesy of the Institution 
for permission to reproduce here the figures representing the 
construction of the larger of the two, as also one of the torsion 
dynamometers by the same constructor in a subsequent 
chapter. Fig. 85 is sufficient to show the operation of this 
machine. Two pulleys D and B are mounted on the same shaft 
C, B being keyed and D running loose upon the shaft. Power is 
communicated to the pulley D by means of a belt, and a second 
belt transfers the power from the pulley B to the driven 
machine. The connection between the two pulleys is effected 
by means of projections J from the pulley D pressing upon the 
ends of two pistons working in cylinders carried by the pulley B. 
These pistons are not packed, but are made a smooth fit, and 
leakage and friction are both immaterial. The pressure 
in the oil behind the pistons is taken by means of the curved 
pipes G to the hollow axle and thence through an axial fixed 
tube, which enters the axle without leakage by means of a 
stuffing-box to the casing N. To this is connected a pressure- 
gauge 0, and also the piston of an indicator similar to those 


182 


DYNAMOMETERS 


used for indicating steam engines. The paper is fed con¬ 
tinuously past the pin by worm gearing in proportion to the 
speed of the shaft. At high speeds the centrifugal force of the 
oil in the pipes G may interfere, but it is possible to balance 
this for one position only of the pistons. For this reason 
Dr. Amsler prefers to use this type at moderate speeds. The 




Fig. 85. 


two dynamometers were designed for torques of 50 and 150 
metre-kilograms (4,340 and 13,020 inch-pounds) respectively.] 


[Moore’s Direct-Reading Electrical Dynamometer.] 

[An interesting and original method of employing electrical 
means not only to measure the angle through which a spring 
connecting the two shafts of a transmission dynamometer is 
twisted, and hence the driving torque, but also automatically 
to multiply this by the speed, so that the power being trans¬ 
mitted may be read at any moment upon a voltmeter, is de¬ 
scribed by Mr. C. R. Moore in an article on a “ Direct-Reading 
Electrical Dynamometer ” in the Electrical World (New York) 
for 1912, p. 449. 

Each shaft carries an alternator with a two-pole field magnet, 






























































TRANSMISSION DYNAMOMETERS 


183 


and the exciting current sent through the two in series is 
necessarily the same for each. In all other respects the two 
machines are made identical, and they are so designed as 
to give very accurately a simple harmonic wave form to the 
alternating electro-motive force which they induce. The 
perfection of this result is shown by an oscillograph record. 
The two machines are so connected and adjusted that they 
are in exactly opposite phases when there is no torque and 
consequently no twist in the spring. When, however, one 
shaft is transmitting power to the other, the exact opposition 
of phase no longer obtains. In consequence of this the circuit, 
which consists of the two armatures in series and a voltmeter, 
is no longer dead, but an outstanding voltage 
is available to act on the voltmeter ; and this 
voltage is proportional to the torque multiplied 
by the speed, so the readings of the voltmeter 
at once give the power being transmitted at any 
moment, and the two independent readings of 
speed and torque need not be made. Further, 
by the use of a switch, one of the connections 
can be reversed, then the voltmeter which indi¬ 
cates the vector sum of the two separate voltages 
or either voltage may be read so as to ascertain 
the speed. The proof of the proposition is simple. 

Where two equal harmonically varying quanti¬ 
ties having the same period are compounded, 
the resultant is a harmonically varying quantity 
of the same period and of an amplitude which is 
zero when the components are in exactly oppo¬ 
site phase ; which is their arithmetical sum 
when they are in the same phase, and which, when there is 
a small departure from identity or opposition, is in the first case 
very slightly changed, while in the second it is proportional, 
with considerable exactness to the departure from exact 
opposition. 

This may be shown by reference to Fig. 86. Taking the 
two equal vectors OA, OB, nearly in opposite directions, but 
differing from this by the angle 9 , their component is OC, and 
this is equal to 2 OA X sin 9/ 2. 

As, then, 9 changes from 0 to a moderate angle, sin 9j 2 


A 



B 

Fig. 86. 




184 


DYNAMOMETERS 


changes so as to be very nearly proportional to 6, as the 
following figures indicate : 


0 

Sin 0 / 2 . 

Arc 0 / 2 . 

Per cent, error. 

5° 

•043619 

•043635 

•0367 

10° 

•087156 

•087270 

•1307 

15° 

•130526 

•130905 

•2900 

20° 

•173648 

•174540 

•5110 

25° 

•216440 

•218175 

•7950 


Thus, for angles up to 20 degrees the departure from strict 
proportionality is only J per cent., and it is less than f per cent, 
at 25 degrees. OC then is the amplitude of the harmonic 
wave, which is indicated by the voltmeter, and this is propor¬ 
tional not only to the angle 6, but also to the absolute magni¬ 
tude of OA or OB. As these are proportional to the speed 
the indication of the voltmeter is proportional to the torque 
multiplied by the speed or to the power being transmitted. 
By the use of the switch one phase may be reversed, then AB 
instead of OC is shown on the voltmeter ; or one component 
alone may be read, the other being cut out, and this at once 
gives the speed. Provision is made for adjusting the phase of 
one of the alternators so as to obtain exact opposition of phase, 
or this may be adjusted so that the voltmeter reads zero when 
the dynamometer is running, so as to eliminate the small 
losses therein. It will of course be clear that the electrical 
load due to the alternators is infinitesimal, for the only output 
is that needed to actuate a voltmeter ; the load practically 
undiminished is transmitted to a recipient machine. A diagram 
is given showing the extreme accuracy of the straight-line law 
both for speed and for power when tested against a Prony 
brake. The machine is set up in the electrical laboratories of 
the Purdue University.] 

[F. W. Lanchester’s Worm Drive Dynamometer.] 

[F. W. Lanchester’s worm drive dynamometer is in a sense 
a transmission dynamometer, but not in the sense in which 
that term is generally used. The transmission dynamometers 








TRANSMISSION DYNAMOMETERS 


185 


described so far have been appliances to measure the power 
transmitted by some intermediate connection from one machine 
to another, but this machine of Lanchester’s is designed 
to measure directly the efficiency of a worm drive, i.e., the ratio 
of the power transmitted to that received. The valuable 
paper describing this unique machine will be found in the 
Proceedings of the Institution of Automobile Engineers for 
the session 1912—13, Vol. VII., p. 238, and I have to thank 
that Institution for permission to reproduce Fig. 88. 

When power is transmitted from one shaft to another by 
means of worm gearing, the torques in the two shafts, which 



w 



Fig. 87. 


would be in the inverse ratio of their speeds of rotation if there 
were no friction, must, as action and reaction are equal and 
opposite, be impressed in the opposite sense on the worm gear 
casing. Taking a usual case of the worm drive of the back 
axle of a motor car with a reduction in speed of, say, 4 to 1, 
the torque on the worm shaft would be one quarter that of 
the back axle if there were no friction. Actually, as there is 
some friction, it is a little more than one quarter. It is the 
object of the worm drive dynamometer to determine the pro¬ 
portion which the ideal torque \ bears to the real torque l/r, 
then l 1 jr or r/4 is the efficiency of the gear. If there were 
no friction in the gear the casing would simultaneously be 
subject to torques of 4 : 1, about two axes parallel to the axis 
of the worm wheel and of the worm respectively. Fig. 87 is 



























186 


DYNAMOMETERS 


an ideal representation of the worm gear casing seen from below 
with the worm shaft W and the back axle VV. Supposing the 
two shafts to be turning in the directions indicated by the 
arrows round them, the worm being the driver, then the casing 
must be subject simultaneously to two torques about these 
axes, the smaller one of which is represented on the diagram 
by the arrow AB acting at the end of an arm of a given length 
standing up from the centre of the worm shaft, while the larger 
one is represented by the longer arrow AC acting on an arm 
of the same length as the former one standing up from the 
centre of the back axle. These two are equivalent to a single 
force AD acting on an arm of the same length as the other two 
standing up from a point about which the casing may be sup¬ 
posed to be supported. If to the casing a rigid bar EF is 
fastened and this is made to carry another bar FG parallel to 
the back axle, then the two torques upon the casing can be 
neutralised by the application of a single force to the bar at 
the point D' in the line of AD and directly away from the paper 
— i.e., if the casing is so supported as to have any freedom of 
rotation about each of the two axes or about the point A, whioh 
in the plan is their crossing point. With a 4 to 1 reduction 
the distance C'D' would be exactly one quarter of C'A, if there 
were no friction in the gear. As there is some friction, the 
distance CE' at which a single force will neutralise both 
torques must be a little more than one quarter of C'A. In the 
actual machine, of which a photograph is shown in Fig. 88, 
the worm casing is supported on ball or roller bearings 
about the axes of the two shafts and the two distances 
C'A, C'D' are 24 and 6 in. respectively. The heavy weight 
hung from the knife edge D applies a counter-acting torque 
about the two axes simultaneously, and the value of 
the smaller torque may be adjusted by means of the 
screw with head E and counter F attached. Ring bolts are 
secured to the base so as to prevent the heavy weight from 
tilting the frame through more than a small angle about either 
axis. Dash-pots are fitted to damp out vibrations about 
either axis. The shaft on the left-hand side of the photo¬ 
graph is the worm shaft; the shaft of the worm wheel which 
goes out at the back is not visible in the photograph. Flexible 
couplings are fitted to both shafts to allow the necessary 


TRANSMISSION DYNAMOMETERS 


187 



Fig. 88. 






188 


DYNAMOMETERS 


freedom in the casing. In using the dynamometer power is 
applied to the worm shaft by a four-cylinder motor-car engine, 
and the worm wheel shaft is made to transmit its power back 
to the worm shaft through the intervention of a slipping belt 
running just too fast for the worm shaft. In this way the 
engine is only called upon to supply the power lost in the whole 
of the mechanism. The power passed through the gear 
depends partly on the speed and partly on the tightness and 
consequent friction of the slipping belt, and these are capable 
of independent adjustment. 

In making a test the complete swivel framing is first care¬ 
fully balanced with the shafts at rest. The worm is then set 
into rotation and the weight hung at C ', and there adjusted in 
amount until the frame is balanced about the worm wheel axis 
and the steady rod is floating in its eye-bolt. The torque in 
inch-pounds in the worm wheel shaft is then found by multi¬ 
plying the number of pounds in this weight by 24. The knife 
edge is then screwed along to some point E' beyond D' of 
Fig. 87, until the secured steady rod floats in its eye-bolt. 
When this is the case the torques on the two shafts are in the 
ratio of AC' to C'E', whereas if there were no friction it would 
be in the relation of AC' to C'D', and C'D'/C'E' is the efficiency. 

Supposing the efficiency to be 95 per cent., then C'D'/C'E' 
= *95, or since C'D' = 6 inches, C'E' = 6-322 inches 
with efficiency 96 per cent. C'E' — 6-248 „ 

with efficiency 97 per cent. C'E' = 6-186 ,, 

As the position of the knife edge at which the frame floats can 
be obtained with an accuracy of about inch, it is possible 
to determine efficiencies with an accuracy of ^ per cent. 

The results obtained with this apparatus have proved to 
be of the highest value. They have shown that the Lanchester 
worm gear is unsurpassed in efficiency and that unexpectedly 
great pressure may be taken by the worm without loss of effi¬ 
ciency, and that this may reach the high value of 96-8 per cent., 
representing a loss of only 3-2 per cent. The efficiency is 
affected slightly, as might be expected, both by the speed and 
by the torque transmitted ; but for further information on 
the results the reader is referred to the original paper. It may, 
however, be well to mention that the friction with different 
oils and at different temperatures was found to depend upon 


TRANSMISSION DYNAMOMETERS 


189 


something besides the viscosity, and pure mineral oil was not 
so good as animal or vegetable oil; in fact, the frictional losses 
were in some cases nearly double as great with mineral oil as 
with animal or vegetable oils. 

It is clear that the Lanchester machine could be modified 
so as to test the efficiency of bevel gearing.] 

[Draw-Bar Dynamometers.] 

[The author has left no account of draw-bar dynamometry, 
such as is practised in the dynamometer coach of an experi¬ 
mental train. Strictly this is “ dynamometry,” and it comes 
more nearly under the heading of “ transmission dynamometers ” 
than any other. He acknowledges however on page 15 the 
permission given to him to reproduce a figure of the dynamo¬ 
meter car of the Great Western Railway. I do not know 
whether the omission by the author to proceed with this was 
intentional, as taking him too far from his main subject, or not. 
I do not care, therefore, to do more than mention the existence 
of this class of testing and to refer in particular to two recent 
publications. The first is by Prof. W. E. Dalby, in the Pro¬ 
ceedings of the Institution of Mechanical Engineers, 1912—14, 
in which the observations made in a trial run are treated very 
completely by graphical representation. The second will be 
found in a series of articles in the Engineer for the year 1913 
by Mr. C. R. King on “ The Dynamometry of Locomotives, 
with special reference to the Use of Super-heated Steam.”] 


CHAPTER XI 


TORSION POWER-MEASURING MACHINES OR TORSION METERS 

PAGE 

The necessity for this kind of Power-Measjirer . . . . . .190 

Remarks by Mr. Archibald Denny . . . . . . . .190 

The Principle underlying the construction of Torsion Power-measuring 

Machines ........... 190 

Method of calculating the Torsion, the Transverse Elasticity G being known 192 
Experimental Determination of G for a small rod ..... 193 

Recent forms of power-measuring machines of the Torsion 
type, designed to measure the shaft horse-power delivered by 
marine engines, have been the outcome of the difficulty 
experienced in indicating a steam turbine in a satisfactory 
manner. The necessity of employing such machines is well 
and clearly shown in the first paragraph of a paper read on 
March 21, 1907, by Mr. Archibald Denny before the Institution 
of Naval Architects. He writes thus :— 

“ When the suitability of the turbine method of propulsion for 
commercial work was proved by the success of the King Edward, 
built by my firm in 1901, it became apparent to us that it would be 
highly desirable to have a method of ascertaining the hors 3-power 
transmitted by the turbine shafts to the propellers. 

“ Until that problem was solved we could only work from the boiler 
to the propeller, and the efficiency of the turbine and the propeller 
must be lumped together. It is not possible to ‘ indicate ’ the turbine 
in the same way as is done for a piston engine, although I may say that 
a fair approximation can be got by ascertaining the fall of pressure 
through successive expansions by means of pressure gauges fixed to 
the turbine casing.” 

Before describing the torsion meters of different inventors 
we may briefly examine the principles underlying the con¬ 
struction of power-measuring machines of this type. 

If by means of a shaft of elastic material (well within its 



TORSION POWER-MEASURING MACHINES 191 


elastic limit) the energy of a prime-mover is imparted to a 
machine such as a rolling mill, or to the propeller of a steam¬ 
ship, and the following quantities are known—namely, the 
twisting moment of the elastic shaft T, in statical inch-pounds, 
the number of revolutions of the shaft per minute N, and the 
angular motion of the shaft 2?rN—then the horse-power 
transmitted is 

“-sSb-***™"- 

The function of this type of machine is to show, by some 
means, the angle of torsion, which represents a given statical 
twisting moment, when the shaft is rotating under load. For 
effecting this, optical, mechanical, and electrical methods have 
been pressed into service. The angle of torsion 6 for a given 
statical twisting moment T is first found when the shaft is at 



rest, and from this determination other independent values 
of 6 and T are known, since 6 T. 

One method whereby the calibration may be made is illus¬ 
trated diagrammatically in Fig. 89, in which AB is the shaft, 
supported on centres C, C. The weights W v W 2 act on the shaft 
through the arms D v D 2 . A tubular sleeve is fixed to the shaft 
at Si, and another short sleeve is fixed to the shaft at S 2 . In 
order that an exactly known length of shaft may be dealt with, 
the sleeves are fixed on the shaft by means of three equidistant 
pointed set screws which engage with the shaft on a line traced 
round it. In some of the earliest experiments on torsion this 
was the method employed for fixing the sleeves on a measured 
length of shaft. Recently annular edges have been employed 
to fix the sleeves, the sleeves being kept in position while they 
are clamped on by bolts and distance pieces (the method used 












192 


DYNAMOMETERS 


in the Hopkinson-Thring torsion meter). When these are 
removed, the two sleeves are left on the shaft in exact position 
at a known distance l apart. Known weights W v W 2 are 
caused to act on the shaft and the deflection noted where the 
edges of the sleeves meet, so that a known twisting moment is 
indicated by the angle of torsion due to it, which can be read. 
Now, from the law connecting the twisting moment with the 
angle of torsion, we know that when the angle for any other 
twisting moment is read the moment is at once known, pro¬ 
viding always that the twisting moment is well within the elastic 
limit of the material of which the shaft is made. Since the 
relative motion between the adjacent ends of the sleeves is very 
small, the reading is usually effected by means of some magni¬ 
fying device, either optical, mechanical, or electrical. 

The angle of twist in the case of a torsional ergometer is best 
found by actual trial when the instrument is set up. But for 
the purpose of finding 6 very approximately, as an aid in 
designing, the following method of calculation maybe employed. 
The angle of twist 6 can be found from the dimensions of the 
shaft transmitting a given H.P. at a given number of revolu¬ 
tions per minute, thus :— 

Let— 

the diameter of the shaft = d inches, 

the twisting moment = T in statical inch-pounds, 

the length of shaft under torsion = L inches, 

the revolutions per minute = N, 

transverse elasticity * = G in millions of pounds per 

square inch, 

then the angular velocity = 27 tN 

and the horse-power transmitted is 


and 


H.P. = 


2ttNT 


T = 


12 X 33,000 
33,000 X 12 X H.P. 
2rrN 


(1) 

( 2 ) 


now T = fZ h where / = the greatest shearing stress 

„ Z t = torsional modulus of the shaft derived 
from the dimensions of the shaft; 


* This term G has been called “ the modulus of rigidity.” By Prof. Unwin it 
is called “the coefficient of transverse elasticity” (“Machine Design,” Part I. 
p. 50, 1909). 




TORSION POWER MEASURING MACHINES 193 


for a cylindrical shaft diameter d, 


Z, = ~ d 3 = 0-196 d 3 , 

for a tubular shaft 




_ 77 - 


- d 4 

— = 0*196 


df - d 2 * 
d 1 


16 d x 

where d 1 and d 2 denote the outside and inside diameters. 
For a cylindrical shaft 

2TL 2TL 32TL 


e = 


GZ t d 


G^d 3 d 

16 


' Gnd* 


( 3 ) 


Should the reader wish to find G, without very great accuracy 
in the reading of the length and angle of deflection being aimed 
at, the experiment can be made without any special apparatus 
on a small shaft mounted in a back-geared lathe, the fixed end 
of the shaft being held in a three-jaw chuck and the gear 
locked to prevent rotation. Near the ends of the shaft metal 
bosses carrying pointers of thin sheet steel are clamped. The 
bosses should be short and the section such that only an annular 
edge embraces the shaft. The edges of the steel pointers are in 
the plane of the annular edges of the bosses. This construction 
provides an easy way for placing the plane of the pointers at a 
given distance from fixed points on the rod. Beyond the boss, 
at the back-centre end of the lathe, a pulley is fixed on the shaft 
embraced by a flexible belt, such as webbing, from which weights 
are suspended to produce the desired torsion. The edges of 
the steel pointers move against vertical scales. When the 
shaft is unloaded the pointers should be horizontal, and the 
points in which they cut the vertical scales taken as the zero 
of each. The weights are put on in front of the lathe and the 
difference of the readings taken. The pointers should reach 
about 30 inches from the axis of the shaft towards the back of the 
lathe bed. For finding the tangent of the angle of deflection, 
and from it the circular measure of the angle, it will be found 
convenient to employ metric scales, the distance from the axis 
of the shaft to the vertical scales being also measured in milli¬ 
meters. In an experiment in which the shaft and apparatus 
were mounted as described the length of the torsion arm, 
namely, the radius of the pulley = 5-27 inches ; the load on its 
end == 2-2046 pounds ; the torsional moment = 5-27 X 2-2046 
d. Q 






194 


DYNAMOMETERS 


inch-pounds ; the distance from the fixed end to the boss 
between the pointers L = 25*59 inches ; the radius of the small 
shaft r = dj 2 = 0*1165 inch ; tan 9 = 0*09327 ; 6 in circular 
measure = 0*09308 ; rr = 3*14159. 

The connection between the quantities involved is embodied 
in the equation 

32TL 


G = 




putting the values found into this equation we find that 
G = 10*512 X 10 6 pound inch square. 

From equations (2) and (3) 

2ttNT 


H.P: 


T = 


12 X 33,000 

0G77# 

32L * 


If the torsional angle is read in degrees and written 6°, it 
must be converted to circular measure by the divisor 57*3, so 
that 

2tt 2 G 


h.p = ^ 4 x 


L 

0°Nd 4 


12 X 33,000 X 57*3 X 32 


X 0*3262. 


So that in each dynamometric experiment on the same shaft 
only 9° and N have to be recorded. 








CHAPTER XII 


TORSION POWER-MEASURING MACHINES OF DIFFERENT 

INVENTORS 

PAGE 

Hirn ............. 195 

Jervis-Smith 

Mechanical method of read'ng the Angle of Torsion .... 196 

Optical methods of reading the Angle of Torsion . . . .197 

The Rotostat........... 198 

Lord Rayleigh, quotation on this subject . . . . . .199 

Application of the Rotostat for comparing the speed of two engines . . £00 

Jervis-Smith. Another optical method of reading the Angle of Torsion . 201 

Jervis-Smith. Electrical method of reading the Torsional Angle . . 202 

Mr. Archibald Denny on the electrical method of reading the Torsional Angle 203 
H. Frahm’s Torsion Meter ......... 206 

The Torsion Meter of Dr. Fottinger, with Efficiency and Power Diagrams . 209 

The Denny-Johnson Torsion Meter.212 

The Torsion Meter of Hopkinson and Thring.212 

[Dr. Alfred Amsler’s Torsion Meter, with comments by H. H. Broughton] . 215 

[Lux]. 217 

[Johnson] ...••••••••• 2 ^ 7 

[Thurston]. 2 ^ 7 

In this form of power-measuring machine, as I have shown, 
the torsional angle of a shaft must be known while it is rotating 
and energy is transmitted by it. Hirn * appears to have been 
the first to employ this direct method of measuring power. 
The torsional angle in his machine is shown by means of a 
pointer deflected by means of differential cog-wheel gear, the 
number of cog-wheels being eight. 

At each end of a known length of shaft a cog-wheel is fixed ; 
these are in gear with cog-wheels keyed on two small counter¬ 
shafts placed parallel to the main shaft, rotated in opposite 
directions by means of an intermediate cog-wheel. Bevel 
cog-wheels of a differential gear are keyed to these shafts, and 

* “ Les Pandymometres,” par G. A. Hirn : Paris, Gautier Villars, 1876. 

O 2 







196 


DYNAMOMETERS 


a pointer is fixed to the frame which carries the intermediate 
bevel wheel, the axis of which is at right angles to the axes of 
the two former ones. 

The differential gear, consisting of two bevel cog-wheels, one 
loose the other fixed on the same axle, each being in gear 
with a third bevel wheel, the axle of which is at right angles 
with the former axle, appears to be the invention of H. Holds - 
worth, who patented the device (1826) in connection with the 
winding machinery used in the manufacture of cotton yarn. 
Since that date the method has been constantly employed in 
many different kinds of machines, such as the driving 
mechanism of telescopes, the differential governor of Siemens, 
and the driving gear of traction engines, tricycles and motor 
cars. In the case of vehicles it enables the two driven 
wheels to rotate with different angular velocities while they 
are both being driven in the same direction. The mechanism is 
commonly known as “ Jack in the box.” But to return to 
the torsion machine of Hirn. When the main shaft revolves 
without torsion, the rotation of the two bevel wheels of the 
differential gear is equal, but if torsion is set up in the main 
shaft, one cog-wheel advances on the other, and the frame of 
the intermediate bevel wheel is deflected and with it the 
pointer, which shows the angle of torsion. 

The end of the pointer is hinged to a light lever, which 
actuates the recording wheel of an integrator of the type 
employed by Morin, so that by this means the power trans¬ 
mitted during long periods of time may be estimated. This very 
interesting original paper should be read in order to appreciate 
the genius of Hirn. 

In 1893 I devised a differential gear for showing the torsion 
of a shaft transmitting work, in which only four wheels and 
a flexible joint were employed. In Hirn’s apparatus eight 
wheels were required. 

The machine was exhibited at the Soiree of the Royal 
Society (exhibit 22, p. 11 Descriptive Catalogue, Conver¬ 
sazione, Royal Society, May 2, 1894). 

RQ is the shaft (Fig. 90), LM its bearings, ABCD are 
gun-metal wheels of equal diameter made with involute 
teeth. The rod K below the shaft is carried in the bearings 
BN. 


TORSION POWER-MEASURING MACHINES 197 


The wheel D is carried on the arm E, which is free to rotate 
about the axis of the shaft on a concentric sleeve ; the wheel D 
is driven by means of the double flexible joint FG, not a 
Hooke’s joint. 

If the system be rotated when no work is being transmitted, 
then the pointer P remains at the zero of a divided dial, but 
when the shaft is subjected to torsion the point P is deflected 
through an angle proportional to the torsional angle in a plane 
perpendicular to the plane of the paper. Also, since the axis 
of the wheel B is fixed when the system is rotating, the pointer 
P indicates the angle of torsion. The arm E can be connected 
to an integrator by means of which the whole work done during 
any time may be estimated. This form of differential gear 
appears to require the least number of moving parts. The 


* rM 


Vn Q 


' '11 

& - c=L ir /r - 

r* 


P i 

Fig. 90. 


differential method of indicating the angle of torsion of a 
propeller shaft has been used by the author, and the results 
obtained show that the apparatus is practically dead-beat. 
The gear may also be used to indicate electrically when a 
certain limit of torsional angle is exceeded. 

Two optical methods of reading the torsion of a wire or 
shaft while rotating were shown at the Royal Society, May 2, 
1894. 

The first depends on the phenomenon of the retention of an 
image by the organs of vision for a fraction of a second. The 
second method depends on the reversal of the motion of the 
image of a rotating object by means of a combination of 
mirrors revolving at half the angular velocity of the object 
and in the same direction. 

The first method is illustrated by an application of the 
optical principle to an instrument used to measure the work 
done in rotating a copper cylinder in a magnetic field. The 










198 


DYNAMOMETERS 


arrangement of the apparatus is shown only diagrammatically 
in Fig. 91. 

A copper cylinder C is attached to a torsion rod or wire SS ; 
this wire is attached to the upper end of a tube which runs 
in the bearings BB ; the tube carries a cylindrical scale DD 
at its lower end, divided at its edge into degrees. The torsion 
rod is furnished with a double pointer PP, which is turned 

up at its ends so as to 
w pass closely over the 

divisions of the scale on 
the cylinder ; the torsion 
wire at its lower end 
passes through an agate 
collar A fixed to the 
tube ; by means of the 
pulley W the whole 
system is rotated about 
a vertical axis. 

The tube T carries an 
electric break K, and the 
primary coil of the induc¬ 
tion coil I is twice closed 
and opened at each revo¬ 
lution. The secondary 
wires go to a Leyden 
jar J and a spark at M 
illuminates the pointers 
and scale ; the light due 
to the spark is concen¬ 
trated by the lens L. 
Thus at whatever speed 
the system is rotating the spark is always made at the right 
instant, and thus the position of the pointer can be easily read. 
A small vacuum tube may be used at M, but the illumination 
is not so good as that due to the spark. This method of 
illumination enables the experimentalist to use the torsion 
balance while rotating at any required velocity. 

The name “ optical rotostat ” has been given by me to a 
combination of mirrors so arranged and moved that a rotating 
object viewed by reflection from their surfaces appears to 




















TORSION POWER-MEASURING MACHINES 199 


be at rest. It is described in Engineering thus :—“ The rotostat 
is an instrument for optically bringing to rest the image of 
revolving objects, such, for example, as the spokes of a revolving 
wheel. ” The instrument, used in conjunction with a torsional 
work-measuring machine, was exhibited at the same date 
(May 2, 1884) at the Royal Society. Since that time it has been 
applied to a variety of uses. I find that prior to my experi¬ 
ment an optical arrangement for viewing mixed colours had 
been employed by Lord Rayleigh. In this case the coloured 
discs were fixed, and their mixing was produced by the rotation 
of an inverting prism. The description of the method is most 
interesting, and I give it at full length.* 

“ In conclusion I will describe an apparatus by which it is possible 
to observe these colour-matches without rotating the disks. . . . The 
idea, which I carried out . . . was to spin an image of the disks instead 
of the disks themselves. An inverting prism was mounted in a tube which 
could be made to rotate. The axis of rotation is adjusted so as to point 
accurately to the centres of the disks mounted as usual. An eye applied 
to the prism sees the disks undisplaced as a whole, but inverted by reflec¬ 
tion. As the tube rotates, the image of the disks rotates also, and with 
double angular velocity. When the speed is sufficient, the colours 
lying on any circle concentric with the disks are blended exactly as if 
the discs themselves revolved.” 

The author was unaware of the existence of this method 
when he used the combination of mirrors for reading the dial 
of the ergometer when rotating ; although in each experiment 
practically a reversing prism is used, yet they differ in this 
respect—namely, that in the experiment cited the instrument 
is used to mix that which is seen through it, whereas in the 
author’s application of the reversing mirrors or prism the 
apparatus is used for optically bringing to rest a divided scale 
rotating before it, by rotating it at half the speed of the object 
viewed and in the same direction as the object is rotating. If 
the reflector is a prism this is mounted in a tube which can 
rotate about its own axis. A ray of light passing along this 
axis is reflected as shown by the broken line DE from the 
face BC of the prism ABC. (Fig. 92.) 

* British Association Report, September 2, 1881, page 46. 


200 


DYNAMOMETERS 


I find that the rotostat is capable of another useful applica¬ 
tion, namely, to show when two engines are running at the same 
speed. The reflecting prism is rotated by one engine, while a 
disc with a line ruled on it as a diameter is rotated at half 
the speed of the former by another engine. If the two engines 
are running exactly at the same speed, the line does not appear 
to move, but if one gains or loses on the other, the line is 
rotated at a rate proportional to the difference of their speeds. 

[I used this device in order to 
bring the rotating film of the 
rainbow cup * to apparent rest, 
and showed how, with slight errors 
of centering, curious trochoidal 
disturbances are set up. The re¬ 
flecting prism used as described 
by the author is not really exactly equivalent to a plane mirror, 
for it reflects a conical bundle of rays with its axis parallel 
to the reflecting surface (Fig. 93), bringing those rays that 
come from below up over the reflecting surface, by which they 
are totally reflected, and then allowing them to continue their 
path below this plane again. This, of course, is impossible 
with a plane mirror. As it is important that the reflecting 



A 

✓ 



prism should be accurately placed in its tubular support, not 
only with the long edges of the reflecting plane parallel to the 
axis, but with this plane the right distance from the axis, I 
give the position calculated for the ordinary refractive index of 
glass, which is 1-5. With a right-angle prism of such glass 
the reflecting surface should be distant from the axis of rotation 
by an amount equal to T125 of the length of the hypotheneuse 
face. All that part of the prism near the right angle, which is 

* Proceedings of the Royal Society, Vol. LXXXVII., 1912, page 349. 











TORSION POWER-MEASURING MACHINES 201 


more than double this distance from the reflecting face, shown 
dotted in the figure, is outside the limit of rays entering the 
prism parallel to the axis which can be reflected from the 
larger face and is useless. If the reflecting face is not the correct 
distance from the axis of rotation, a central ray parallel to this 
acquires a lateral deviation, as shown by the dotted ray path 
in the figure. If the prism is so set that its reflecting surface 
is not exactly parallel with the axis, an angular deviation 
results, while if the axis about which the prism turns is not 
directed towards the centre of the rotating object which it is 
sought to bring to apparent rest, the object will appear to 
turn about an eccentric point at twice the speed of rotation 
of the prism, whereas the other errors give apparent motions 
at the same speed as the prism and the combination of errors 
leads to trochoidal curves, which, while full of interest, destroy 
the illusion.] 

During certain experimental work in which it was necessary 
that the energy transmitted by a rotating shaft should be known, 
I devised in 1909 the following method of reading the angle of 
twist of the shaft, and found that it gave good results. It 
is easily applied and might be used for other similar purposes in 
the mechanical laboratory. Clear readings can be taken from a 
pointer moving over a circular dial which reflects light, while 
it rotates about a diameter. The optical principle involved 
is similar to that of the Thaumatrope of Dr. Paris, in which 
on one side of a card the head of a man was painted, and on 
the other side a hat. When the card was rotated by means 
of twisted strings attached to the opposite edges of the card, the 
head and hat appeared as one picture—the rationale of the 
experiment being that the picture of the head is retained by 
the organs of vision until the hat appears, the two separate 
impressions thus making one picture. In my apparatus the 
reflecting dial, made of mirror glass, is fixed so that its plane 
is parallel with the axis of the shaft or of the spiral spring, the 
angle of twist of which is to be measured. The mirror is per¬ 
forated in the centre, and through the perforation the pivot 
which carries the pointer passes. The pointer is deflected (by 
means of connecting links attached to the shaft, and also to a 
sleeve fixed to the shaft) through an angle proportional to that 
of the twist of the shaft. 


202 


DYNAMOMETERS 


A parallel beam of light is projected on to the mirror dial 
by means of two plano-convex lenses, as used in a projection 
lantern, the source of light being an arc lamp slightly shielded 
by ground glass. The image of the pointer, moving over the 
divided scale, can either be viewed direct by one person by 
reflection, or, which is far more convenient, the image can be 
projected on to a screen, by means of two achromatic lenses, 
and then it may be viewed simultaneously by several observers. 
This latter method of viewing the pointer is preferable to the 
former one, which is rather fatiguing to the eye owing to the 
intermittent flashes. Even when the speed of the shaft is 
slow, about 300 revolutions per minute, and the flashes occur 
at intervals of one-fifth of a second, the image of the pointer is 
clear and well defined. I have applied this optical method of 
reading a moving dial to a torsion work-measuring machine 
placed between an electric motor and a dynamo feeding an 
arc lamp. The best way of reading the torsional angle of a 
shaft is undoubtedly by means of an automatic record or trace 
made on a paper-covered cylinder driven from the shaft by a 
scribing pen the motion of which is proportional to the force 
ordinate at any instant and hence to the angle of torsion. 
The speed of rotation of the cylinder is reduced by means 
of gearing, so that a record extending over a long period of 
time may be taken. 

In some cases such an elaborate method of reading the 
torsional angle is not required, and the optical method I have 
described is sufficient for those cases in which only rather 
small powers are dealt with, as, for example, in aeroplane 
engines and motor-launch internal combustion engines. 

Electrical Methods of Reading the Torsional Angle 
of a Shaft. 

The February number of the Philosophical Magazine , 1898, 
contains the description of an electrical method devised by 
myself whereby the angle of torsion of an elastic shaft was 
determined while rotating. The method was applied to find 
the torsion of a long shaft used in driving a dynamo, and also 
the torsion of a solenoidal spring used as a flexible shaft to drive 
propellers of different forms under different conditions of 


TORSION POWER-MEASURING MACHINES 203 


immersion. Two discs of insulating material were fixed near 
to the ends of the shaft. Each disc was furnished with a 
narrow contact-piece at its edge, connected to the shaft and 
two metal brushes (one of which was stationary and the other 
moveable) pressed on the discs as they revolved. An electric 
circuit was formed 'including the shaft, a line-wire, a battery, 
and a telephone. When the shaft was at rest and the brush 
was touching the contact-piece, on the disc at the driven end 
of the shaft, the brush at the driving end of the shaft was then 
adjusted by being moved on an arm which rotated about the 
axis of the shaft, so that on making or breaking the circuit a 
click was heard in the telephone ; this position of the arm and 
brush was marked as the zero from which the angle of torsion 
was reckoned. The shaft was then fixed at the driven end 
and subjected to a known statical torsional moment, and the 
brush rotated till a click was heard on making or breaking the 
circuit ; thus a dial indicating the torsion of the shaft was 
calibrated. Since the angle of torsion is proportional to the 
statical moment, within certain limits, the dial was easily 
calibrated when one or more points on it had been determined. 
When the power of an engine was transmitted through the 
shaft to a dynamo, the engine being at one end of the shaft 
and the dynamo at the other end, the arm carrying the brush 
was moved over the divided dial till the click was again heard 
in the telephone. The angle through which it was moved 
was thus the angle of torsion of the shaft. And the value of 
any torsional moment was found from the indicated angle of 
torsion. If the torsional moment in statical inch-pounds is T, 
the number of revolutions per minute N, and the horse¬ 
power transmitted H.P., 

2ttNT 


H.P. 


33,000 X 12' 


Mr. Archibald Denny, not at the time of his experiments 
knowing of the existence of the paper I have mentioned, 
worked on almost exactly the same lines on workshop shafts, 
and also applied the method to the steamship Queen Alexandra , 
as described in a paper read before the Institution of Naval 
Architects, March 2, 1907. 

The experiments of Mr. Denny are of so much value and 
interest that I have given a description from the paper cited, 



204 


DYNAMOMETERS 


which shows further developments tending to great accuracy 
of reading the torsional angle :— 

“ Some fifteen years ago we had made numerous experiments with 
factory shafting, endeavouring to ascertain the absolute torsion of a 
shaft while running, and it therefore immediately occurred to me that 
this was the proper direction in which to attack the problem. We had 
tried various methods, principally using pierced discs and beams of 
light, but with very partial success. We had not tried any method 
involving the use of electricity, and I therefore arranged for experiments 
to be made by this method on one of our factory shafts. The first 
trials were made by fixing discs on the shaft at a considerable distance 
apart, so as to get a reasonable amount of torque. The discs were of 
insulating material, and each had a contact point arranged at its 
periphery in such a manner that the point made momentary contact 
with a metal tongue or brush once in every revolution of the shaft. 
The contact points were connected to the shaft and the metal brushes 
to a battery and a telephone receiver. The method adopted was first 
to adjust the brushes, so that both made contact with the points 
simultaneously when the shaft was revolving but transmitting no 
power. When transmitting power the shaft was, of course, subject 
to a certain amount of torsion, and thus the brushes were put out of 
simultaneous contact. One of the brushes was then moved round its 
disc concentrically, until simultaneous contact was once more estab¬ 
lished. The amount of this shift gave a measure of the torque on the 
shaft, and to ascertain the correct amount of this shift the telephone 
receiver was placed to the ear, no sound being heard except when both 
brushes were in contact with the respective contact points, when a 
loud ‘ tick ’ was heard. The principle was thus of extreme simplicity, 
and the method of carrying it out seemed at first equally simple ; 
indeed, I may say that this first rough apparatus, which was quite 
successful, only cost a few shillings to make. We then set about 
making more accurate and elaborate apparatus on the same lines to be 
fitted to the Queen Alexandra, which was nearly ready for trial, with an 
assured hope of getting satisfactory results. 

“ The factory shaft on which we made the original experiments ran 
about 120 revolutions per minute, but the revolutions of the Queen 
Alexandra’s side shafts were over 700, and when we came to make 
experiments at this high speed we found the new apparatus was useless, 
as no certain sound could be got. We tried many forms of contacts, 
and after numerous experiments we did succeed in the Queen Alexandra, 
with revolutions about 750, in getting some fairly consistent results ; 
but it was impossible to be quite certain of the exact point at which the 


TORSION POWER-MEASURING MACHINES 205 


make and break in the circuit took place, and we were never quite sure 
of our results ; still, we had made a great step in advance.” 

(Probably this difficulty of adjustment was due to the 
inherent property of a shaft, when driven by a recipro¬ 
cating engine at high speed, of oscillating about its axis at 
a certain definite rate for a given rate of rotation. These 
oscillations are imposed on the torque of the shaft while 
rotating, and under certain conditions have a marked lag, 
with respect to the torsional moment at any instant, a point 
clearly shown by Dr. Fottinger, F.J.J.S.) 



“ Mr. Charles Johnson, a member of our staff, who assisted in working 
out this problem and was closely connected with it from the first, 
thoroughly appreciated the difficulties, and realised the desirability of 
getting away from the unreliable rubbing contact, and he ultimately 
succeeded in solving the problem in a most ingenious way. 

“ Fig. 94 shows his original solution. Two gun-metal wheels, A and 
B, were fastened to the shaft at a definite and known distance apart, 
the distance being as great as possible. On each wheel a permanent 
magnet, with a sharp chisel-shaped edge, was fixed radially at the 
periphery of the wheel and with the sharp edge parallel to the shaft. 
At one end a soft iron electromagnet C, wound with fine wire, similarly 
chisel-shaped, was fixed, so that the moving magnet passed directly 
over the electromagnet once in each revolution. At the other end a 
similar electromagnet D was mounted on a screwed sector, and wires 
from these electromagnets were led to a differentially-wound telephone 
receiver. If the shaft revolved without transmitting power, the 
permanent magnets passed these electromagnets simultaneously, and 















206 


DYNAMOMETERS 


currents of electricity generated in each coil passed through the tele¬ 
phone receiver, but, the currents being equal and opposite, no sound 
was heard. When the shaft transmitted power, the permanent magnets 
passed the electromagnets at different times, and hence a sound was 
heard in the receiver. By turning the hand-wheel shown in diagram, 
a new position of silence could be obtained, when it was evident that 
the two permanent magnets were again passing the electromagnets 
simultaneously, and the amount of torque could be ascertained from 
the reading of the sector screw.” 

A further development of this machine and apparatus is 
described under the heading, “ The Denny-Johnson Torsion- 
Meter.” 

Most interesting and valuable researches have been made by 
Mr. Hermann Frahm on the torsional stresses developed in pro¬ 
peller shafts when running on ships. The work, which began 
in 1899, has led to the invention amongst other things, of the 
now well-known Frahm Speed-indicator, the action of which is 
based on resonance. A large number of minute white squares 
form the ends of thin steel reeds of different pitch ; these are 
clearly visible on a dark background. These steel reeds are 
attached to a shaft which is made to vibrate by means of an 
electromagnet, the current being supplied from a small alternate 
current dynamo of the induction type, driven by the engine 
the speed of which is to be known. The vibration is imparted 
to all the reeds, but those reeds only whose natural period of 
vibration synchronises with the period of the alternate current 
are thrown into vibration sufficient to be seen. This instru¬ 
ment may be placed at any convenient distance from the 
engine, and out of reach of other disturbances. 

Mr. Frahm attacked the problem of discovering why pro¬ 
peller shafts were apparently exposed to stresses far in excess 
of what was generally supposed by marine engineers. It has 
been the case that propeller shafts have been fractured in a 
quiet sea, while such fractures did not appear to be due to 
defective material, nor did it appear likely that they could be 
due to couples, caused by steam pressure, since such forces 
seldom reached a dangerous value. 

In November, 1899, Messrs. Blohm and Voss began an 
experimental investigation of the subject, which was con¬ 
ducted by Mr. Hermann Frahm. Since the distance between 


TORSION POWER-MEASURING MACHINES 207 


the prime-mover and the screw is usually great, the propeller 
shaft could not be regarded as a rigid body : it is in fact a 
kind of spiral spring constantly changing in torsion as power 
is being transmitted by it when driven by any reciprocating 
engine. The matter would be different if the shaft were driven 
either by an electric motor or by a turbine. The torsion of the 
shaft would be then practically constant. But when the source 
of power changes, so also must the torsion of the shaft. But 
the changes in the torsions will not be proportional to the 
torsional stresses, as commonly assumed. It would be 
exceedingly difficult to predict what dimensions such changes 
would have. The torsional stresses in the shaft both as to 
magnitude and variation had to be found first. This was 
done by measuring in one revolution of the shaft, step by step, 
the torsions at the instant, in their absolute amounts. The 
torsional stresses could then be estimated. The next step was 
to obtain simultaneous readings of the changes of velocity of 
the whole system, both for the engine and the screw. After 
many preliminary experiments the following methods of work¬ 
ing were adopted:— 

Thin sheets of zinc foil were wrapped round the flanges, 
which were as far apart as possible. A scribing point of 
platinum, carried by a lever, pressed against each zinc foil, 
the pivot of the lever being supported on a nut on a screwed 
spindle placed parallel with the propeller shaft. An electric 
motor, the speed of which could be regulated, was placed close 
to the flange. The shaft of the motor carried two equal 
contact discs which made and broke the current in two inde¬ 
pendent circuits. These were led from the positive conductor 
to the contact-breakers and the platinum points through 
resistances. The zinc foil was coated with a black oxide ; 
this was removed by the platinum point as long as the current 
acted. The method of making the experiment was as follows. 
When the high-pressure piston was at its highest point, the 
engine was stopped and the exact position of the platinum 
points marked, and this was the zero position, and in order to 
obtain this point exactly and as far as possible free from the 
friction of the bearing of the shaft one mark was made when the 
engine was stopped after moving in one direction and another 
made after moving the engine in the opposite direction ; the 


208 


DYNAMOMETERS 


mean position between the two marks was taken as not far 
from the true zero. 

The engine was run for some time before the experiments 
were commenced. The electric interrupter was then made to 
run at the correct speed and the electric circuits were closed. 
The levers were then, at a given signal, brought down on to 
the zinc foils and again removed at another signal ; during this 
time spiral curves were drawn on the zinc foils, broken up at 
definite distances by the breaking of the current. The breaks 
gave data for plotting velocity curves for the two flanges, 
equal time spaces being marked by the beginnings of the 
breaks. In order to plot the velocity curve these distances, 
as marked on the foils, were set up as ordinates, the corre¬ 
sponding abscissae denoting time. The curve plotted through 
the tops of these ordinates is the velocity curve. 

In a second experiment the torsions, and hence the torsional 
stresses, were found thus. The zinc foils were placed in abut¬ 
ment, so that the marks for zero torsion and the top position 
of the high-pressure piston were on the same perpendicular. 
The relative angular displacements of the style marks, which 
corresponded to the same instant, marked the torsion of the 
shaft, which lay between the flanges. These torsions when 
plotted graphically led to a curve which showed the changes 
in the turning moments. The mean turning moments were 
calculated from the mean amplitude of this curve, and hence 
the power given to the propeller (the modulus of elasticity 
of the steel being known). Three shafts were made by three 
different firms—namely, F. Krupp, Bochumer Verein, and 
Gewerbschaft Wilkowitz—and tested at the Royal Mechanical 
Testing Station, Charlottenburg, and the mean value of the 
modulus of elasticity for thrust found by torsion tests. The 
modulus of the three shafts varied very slightly, and equalled 
828,000 kilograms per square centimetre. Using this number 
the effective horse-power transmitted was calculated, and also 
the efficiency of the engines, that is, the ratio of the effective 
horse-power to the indicated horse-power. 

Mr. Frahm states that, so far as he was aware, these were the 
first experiments in which the brake horse-power of engines of 
several thousand horse-power have been accurately found by 
using the shaft as a dynamometer. 


TORSION POWER-MEASURING MACHINES 209 



5 


The Torsion Meter of Dr. Fottinger.* 

In this torsion meter two sleeves or tubes embrace the shaft 
to which they are fixed at their remote ends (Fig. 95). The 
free ends of the sleeves 
where they nearly abut 
are furnished with discs 
which form parts of the 
sleeves. When the shaft 
is subject to twist, points 
on the edges of the discs 
initially opposite to one 
another are displaced 
through the angle of 
torsion for a given length 
of shaft. 

By means of levers 
linked to the two discs I, 

II, this angle of torsion 
is magnified about thirty 
times and recorded by 
means of a tracing point 
on a cylinder which ro¬ 
tates concentrically with 
the shaft but at a con¬ 
venient rate more slowly 
than the shaft, the re¬ 
duction of speed being 
effected by gearing. For 
example, when the ratio 
was 1 to 4, the length of 
one diagram gave the 
curves due to four revo - 
lutions of the shaft. The 
record of no torque is 
a circumferential line 

traced on the cylinder, or a straight line when the record is laid 
out on a plane ; it is the zero line from which the ordinates of 
torque are measured, and the area of the diagram is proportional 






> 

* 


\ 

i, 


1 

J 




£ 


* Schiffbautechnische Gesellschaft, 1903. 


D. 










































210 


DYNAMOMETERS 


to work done. This can be integrated, as already explained at 
p. 64. When the apparatus is used on a shaft driven by a 
reciprocating engine, the varying torque is shown as an undu¬ 
lating line—on one side of the zero 
line when the ship is going ahead 
and on the other side of the zero 
line when going astern. Some idea 
of the reading for a given diameter 
and length of shaft may be formed 
from the following details relating 
to the Kaiser Wilhelm II. 

The diameter of the shaft was 
604 millimetres = 23-78 inches ; 
the length of the shaft was 2,200 
millimetres = 86-614 inches ; 
test radius on discs of the shaft 
was 550 millimetres = 21-653 
inches ; 

revolutions per minute of the 
shaft was 80 ; 

amplitude of curves obtained was 
40 millimetres = 1-574 inches ; 
the magnification of the lever 
system was 27. 

Two loose cylinders were em¬ 
ployed driven by sun-and-planet 
gearing. When the engine employed 
to drive the propeller is either an 
electric motor or a turbine, then the 
mean effective torque is represented 
by a fairly straight line. As speed 
increases, so do troubles due to 
centrifugal forces, and these forces 
had to be contended with and care¬ 
fully balanced: these important de¬ 
tails appear to have been effectively 
worked out by the inventor. By means of this torsion 
meter and ordinary indicator diagrams sixteen in number, both 
the shaft horse-power and the indicated horse-power were found, 
and hence the efficiency of the engine for different values of 






































TORSION POWER-MEASURING MACHINES 211 


-- Effective power 

_ _ Indicated power 

__ Efficiency 



the power. In the case of the steamship mentioned, on her 
first voyage an efficiency of 95 per cent, was reached, and 
on a subsequent voyage an efficiency of 93 per cent. 

In Fig. 96 is shown a curve recorded by the torsion indicator 
(continuous line), from which has been deduced the tangential 
curve for mean speed (broken line). There is apparently 
a curious difficulty in obtaining the true reading of torque 
diagrams, and comparing their ordinates with the tangential 
force, when the engines are running. If the diagram is marked 
O when, say, one of 
the cranks is highest 
and the engine is at 
rest, when the engine 
is working and the 
shaft is stressed, this 
point will be shifted, 
the shaft having tra¬ 
velled past its dead 
point by the amount 
of the angle of torsion 
at the instant when 
scribing point cuts 
the mark. Light can, I believe, be thrown on this rather 
difficult point by making the crank print a mark on the 
diagram, when it is at either its highest or lowest point, by 
electrical means. This would mark the shifted zero. The 
diagrams clearly show the existence of natural vibrations, 
developed at certain shaft speeds. When the torque diagram 
is integrated by means of a planimeter, the mean torque and 
the effective power can be calculated. 

In Fig. 97 the efficiency curve is shown. It indicates a 
satisfactory result : down to one-fifth of the maximum horse¬ 
power the efficiency curve is nearly straight, and at 95 per cent, 
for a range between 20,000 and 10,000 h.p. Points on the 
efficiency curve are found thus. The effective power, as found 
by the torsion meter, is divided by the indicated power, deduced 
from the readings of all the steam indicators. The quotient 
gives the length of the efficiency ordinate. 

Mr. Herman Fottinger’s communication to the Schiffbautech- 
nische Gesellschaft should be well studied by those who wish 

P 2 


2 0 30 40 SO 

Resolution* per minute 

Fig. 97. 















212 


DYNAMOMETERS 


to appreciate very exact and careful work, on the difficult 
problem of dealing with power transmitted by shafts which 
have a natural period of vibration at certain critical speeds. 

The Denny-Johnson Torsion Meter. 

In this torsion meter two sleeves or tubes are fixed on a 
propeller shaft, their ends being at a known distance apart; 
as in some other forms of torsion meters, one sleeve is long and 
the other short. Where they abut they do not touch, but are 
furnished with projecting arms. When the shaft is trans¬ 
mitting power, and subjected to torsion, the two arms move 
relatively to one another, the displacement being proportional 
to the torsion of the shaft, the length of which extends between 
the circumferences embraced by the two sleeves. On one arm 
of a sleeve the primary coil and core of a small transformer is 
fixed, and the secondary coil of the transformer is attached to 
the arm of the other sleeve, while a small air-gap separates the 
adjacent ends of the cores of the transformer. From this it will 
be seen that the air-gap length changes with the angle of 
torsion. The currents through the transformer are so led by 
means of slip-rings to brushes and return wires or earths (if 
the framework of a ship may so be called) that the primary may 
be excited by a small motor-driven alternator, while the 
secondary is connected to an alternate current voltmeter ; so 
that the reading of the voltmeter is proportional to the angle 
of torsion and the voltmeter becomes the torque meter. The 
torque meter is calibrated in fractions of an inch of air-gap 
length and therefore of torsion, and the scales are divided in 
tenths, hundredths, and thousandths of an inch, the smallest 
division being easily subdivisible by eye ; the error of observa¬ 
tion is said to be practically nil. 

The Torsion Meter of Prof. B. Hopkinson, F.R.S., and 
Mr. L. G. P. Thring. 

The principle of this apparatus is a differential one, and 
depends on the observation of the twist of a shaft between two 
adjacent points on it by means of two beams of light projected 
from a fixed and a movable mirror on to a graduated scale. 
The beam of light projected by the fixed mirror determines the 


TORSION POWER-MEASURING MACHINES 213 


zero point of the scale, and that projected by the movable 
mirror indicates the amount of torque of the shaft while 
rotating and driving the propeller of a ship. Although both 
mirrors rotate with the shaft, even at moderate speeds the 




Fig. 99. 



reflections appear as lines of light across the scale, which can 
be easily read. When this form of torsion meter is applied to 
a shaft driven by a turbine engine the reflected line of light is 
steady. Changes of torque would be due only to varying 
resistance experienced by the propeller through the change of 































214 


DYNAMOMETERS 


the position of the blades, in the case of the ship pitching. 
Even when reciprocating engines are employed, a good estimate 
can be made of the imposed torque, which, of course, varies 
during each revolution of the shaft. The construction and 
application of this torsion meter is shown in the two figures 
(98 and 99). A collar A, which is clamped to the shaft, is 
provided with a flange projecting at right angles to it and a 
tubular extension. A sleeve B, also having a similar flange 
and tubular extension, abuts against the collar. The collar 
and the sleeve are rigid, so that when the shaft is subject to a 
twist when transmitting power the flange of B moves relatively 
to the flange of A. This displacement is indicated by a mirror 
called the “ torque mirror,” actuated by a small lever C pressed 
by a spring on to a projection D. The axis about which the 
mirror rotates is at right angles to the axis of the shaft. The 
relative movement of the flanges rotates the torque mirror 
through a small angle, and deflects a beam of light over a 
divided scale, a reflection being received at each half-revolution 
of the shaft, since the mirror reflects from both of its surfaces. 
Fig. 98 shows the shaft in section and the disposition of the 
optical apparatus. 

Prof. Hopkinson recommends a direct calibration of the 
shaft, with the instrument in the position in which it will be 
used before the shaft is put into the ship. This recommenda¬ 
tion is excellent and sound, and more accurate than working on 
the assumption that the modulus of rigidity is absolutely the 
same for each propeller shaft along its whole length. It has 
been shown (“ Notes on the Measurement of Shaft Horse¬ 
power,” Institution of Naval Architects, March 18, 1910) that 
when the modulus of rigidity was taken at 12,000,000 lb. per 
square inch, the stiffness of the shaft so calculated was nearly 
always correct to within about 4 per cent. It is also important 
that the torsion meter should be permanently used on that 
length of shaft on which the twisting experiment was made 
when loaded by means of levers and weights, since the modulus 
of rigidity may vary slightly from point to point along the 
length of the shaft. It appears that experiments have yet to 
be made to investigate the difficult point, namely, whether the 
twist of a shaft is the same without and with the added pressure 
along its axis due to thrust. It must be remembered that the 


TORSION POWER-MEASURING MACHINES 215 


conditions under which the shaft is calibrated by means of 
levers and weights are not exactly the same as those under 
which it normally works. When the shaft is calibrated in the 
works it is subjected to no end thrust such as exists when 
driving a propeller. The question then arises, Is the twist the 
same under the changed condition ? Prof. Hopkinson writes : 
“ It is a question of some importance whether the presence of 
this thrust affects the relation between torque and twist.” 
The problem requires experimental investigation; on full- 
sized shafts the quality sought for would be small, but well 
worth the trouble of finding. 


[The Torsion Dynamometer of Dr. Alfred Amsler.] 

[This instrument was shown at the meeting of the Institution 
of Mechanical Engineers at Zurich on July 25, 1911, and it is 
described and illustrated in the Proceedings of the Institution 
of that date. I am enabled to reproduce one of the figures 
which sufficiently illustrates the construction, a courtesy on 
the part of the Institution for which I thank them. Two 
torsion dynamometers were shown, one with a capacity of 
4,340 inch-pounds, and the other with a capacity of 6,944 inch- 
pounds, or 50 and 80 metre-kilograms respectively. 

Fig. 100 is a longitudinal section of the smaller of the two. 
The torque is transmitted from the coupling F to the coupling H 
by means of the torsion shaft G. The two discs O and N, 
carried by the sleeve A, rotate with the coupling F, while the 
transparent circular celluloid scale U, attached to the disc M, 
moves with the coupling H. P and T are slits in the discs O 
and N through which the observer can see the scale, most con¬ 
veniently by reflexion from a mirror as indicated, the scale 
being illuminated by a lamp. When the machine is running 
fast enough for the persistence of vision to be effective, the 
eye is able to see the scale apparently stationary, the slit T 
defining the particular division, which should be read without 
parallactic disturbance, while a widening of the slit T at one end 
into a window makes it possible to see the adjacent divisions 
and the number of degrees indicated. By carrying the eye 
round the circle the reading of the torsion can be made at any 


216 


DYNAMOMETERS 


desired part of the revolution, so that if the torque is uniform 
the same reading will be obtained in all positions ; but if it is 
subject, as in an engine driven by one or two cranks, to cyclic 
variation this also may be detected and measured. Dr. Amsler 
gives the following figures for the smaller machine. The torsion 
shaft is made of a special spring steel of very high yield-point, 
that is, above 6,000 kilograms per square centimetre (90,000 



Fig. 100. 

lb. per square inch). The length is 40 centimetres (15| inches), 
its cross section is 12 X 12 millimetres (-4725 x *4725 inch). 
With a twisting moment of 20 metre-kilograms (1,736 inch- 
pounds) the torsion is 20 degrees and the stress 5,200 kilograms 
per square centimetre (78,000 lb. per square inch), which is 
well below the yield-point. 

Mr. H. H. Broughton, who spoke in the discussion, has given 
in the Electrician of December 12, 1913, an account of some 
torsion dynamometers that he has set up in Brighton. He 
used both the double-contact system and the illumination of 































TORSION POWER-MEASURING MACHINES 217 


the scale by spark, but in his experience the simple optical 
arrangement of Dr. Amsler is greatly to be preferred.] 

[The Torsion Meters of Lux, Johnson, and Thurston.] 

[In Engineering , November 24, 1911, p. 715, there is an 
account of a development of the torsion dynamometer depend¬ 
ing on the torsion of the shaft by Fritz Lux, the object of 
which is to make a horse-power meter which will integrate 
the power transmitted by the shaft to the propeller of a steam¬ 
ship. The torsion is measured by an electrical arrangement, 
and an electrically-operated counter is so contrived that the 
torsion angle and the angular speed are both factors which 
determine the speed of rotation on the indicating dial. Thus 
the record is one of horse-power hours. One of these was 
being fitted to the cruiser Ersatz Kondor.] 

[On p. 605 of the same volume there is an account also of an 
electrically-worked torsion power indicator by Mr. C. H. 
Johnson, assistant works manager of Kelvin and James White. 
In this the angle of torsion is measured by the electrical effect 
of a sliding contact on a short piece of hard high-resistance wire. 
The contact is at the middle point when there is no torsion, 
and it moves one way or the other according to the direction of 
the torque. This produces a potentiometer effect which may 
be indicated as torque in any part of the ship. In the case of a 
ship with three propeller shafts the connections from the three 
shafts are brought to a single instrument board, where the work 
being done by each shaft may be determined very quickly.] 

[In Engineering, November 8, 1912, p. 627, there is an 
illustrated account of the whirling table for aeroplane and 
propeller tests by Mr. A. P. Thurston, and made for the East 
London Technical College. In this the torque is measured 
by electrical means.] 


CHAPTER XIII 


THE CRADLE DYNAMOMETER 

Jervis-Smith : Ergometer for small electromotors 
C. F. Brackett: Cradle dynamometer .... 
Dr. Drysdale : Cradle dynamometer .... 
Marcel Deprez : Knife-edge suspension .... 
D avis and Shaw: Cradle dynamometer .... 


PAGE 

218 

220 

220 

222 

222 


This form of work-measuring device was employed by the 
author in the year 1881. It was described in the journal of 
the Bristol Naturalist Society, 1883 (“ Ergometer for Small 



Electromotors ”) ; a description will also be found in 
“ Dynamo-Electric Machinery,” by Prof. S. P. Thompson, 
1884, p. 384. This type of dynamometer has been called the 
“ Cradle Dynamometer,” from the fact that in some cases 
the motor, when tested, is supported on a cradle free to 
oscillate. Referring to the diagram Fig. 101, the dynamo or 
motor BD is pivoted concentrically and balanced about the 
axis of the armature E. If this is a motor and the armature 
is driven in the direction of the curved arrow there will be a 
reaction as shown by the arrow P, and the force P X the dis¬ 
tance d is a torque equal and opposite to that experienced by 
the armature. If it is a dynamo the force at P will be in the 
opposite direction, but the arrow shows the direction in which 





THE CRADLE DYNAMOMETER 


219 


a force must be applied to resist the torque felt by the field 
magnets. The invention was the outcome of experiments made 
by me, with a view to make a motor, or a dynamo, regulate the 



Fig. 102. 

current supplied to it or delivered by it. The principle on 
which the machine works is as follows. The bearings on which 
the armature runs were supported on antifriction wheels so 
that the field magnet, which was carefully balanced, was free 








220 


DYNAMOMETERS 


to rotate, the ratio of the diameter of the bearings to the 
diameter of the wheels being about 1 to 7. The axle of the 
armature was attached, in certain experiments, to a small 
propeller shaft, the behaviour of which was to be tested under 
different conditions. When the motor drove the propeller, 
reaction was set up between the armature and the field magnet, 
and the latter was displaced through an angle the magnitude 
of which was proportional to the extension of a spring. The 
spring in some cases took the form of a torsional spring, the 
axis of which lay in the axis of the armature shaft, or of a spring 
balance, as in Fig. 102 ; also, in some cases, a weight fixed 
upon an arm projecting from the field magnet acted against the 
couple due to the field magnet and the armature. The arm 
was so placed that as the angle increased so too did the 
moment of the weight about the axis. When the number of 
revolutions per minute N were known and the effective radius in 
feet R at which the force in pounds F acted, the power was at 
once given by the equation 

TJ 277-RFN 

Horse-power =wro(y) 

where n = 3T4159 and 33,000 is the constant of Watt. 

In the Electrical World, New York, of January 5, 1884, a 
dynamometer working on somewhat the same principle invented 
by Prof. C. F. Brackett, of Prinstown, New Jersey, is described. 
In this machine the cradle holding the motor was constructed 
of steel, and carried on knife edges. This is under certain 
conditions a better way of carrying a considerable weight than 
my own, namely, on antifriction roller bearings. 

Dr. Drysdale has devised a direct-acting dynamometer of 
this type, described in Engineering of November 24, 1905. 
The knife-edge method of carrying a load employed does not 
appear to be as popular as it might be ; some people have mis¬ 
givings as to this method of support. We have but to consider 
the excellent results obtained in huge testing machines, in 
which the loaded beam is carried on steel knife edges, to be 
much encouraged to use the method in many other mechanical 
combinations. Of course, when the motor or dynamo is 
carried on knife edges, the belt drive must be in a vertical or 
nearly vertical line. When antifriction wheels are used, three 
on each side, the belt may be driven from any direction. 



THE CRADLE DYNAMOMETER 


221 


In the experimental plant designed by Dr. Drysdale * the 
principle of the balanced field magnet type of dynamometer 
(see p. 225) is employed. The generator, a four-poled eight- 
kilowatt direct-current machine by Westinghouse, designed to 
give 100 volts between the speeds of 750 and 1,600 revolutions 
per minute, was carried outside its bearings by ball races con¬ 
taining balls \ in. diameter. The field magnet was thus free to 
rotate. Two gun-metal arms fitted to the sides of the motor 
were provided with knife edges from which weights were 
suspended. The arms were fitted with two knife edges, one 
2*625 feet from the axis, the other at 71*4 centimetres from 
the axis. When the machine made 1,000 revolutions per 
minute 2 pounds on the external knife edge represented 
1 horse-power and 3 pounds on the inner knife edge 
represented one kilowatt. Knife edges on both sides enabled 
powers, whether positive or negative, to be measured 
with either direction of rotation of the armature. The 
electrical connections were flexible. Since this machine is 
fixed, the machine to be tested is carried on an adjustable 
slotted table which can be regulated for height by means of 
screw gear. The method of connecting the two machines is as 
follows. An American self-centring chuck forms a part of the 
connecting shaft. In order that the alignment shall be as 
perfect as possible, the end of the telescopic shaft is furnished 
with a small cone at its centre, which fits into the countersink 
of the shaft of the machine to be tested. The sleeve of the 
telescopic shaft passed through a ring supported from the 
floor, a space of in. being left round the shaft when it is 
correctly centred. The clearance when the little cone of the 
shaft was brought up to the counter-sink of the shaft showed 
at once whether one end of the shaft of the machine was on the 
axis. By the application of an ingenious optical method the 
other end of the shaft was brought into correct position, and 
by means of a weight movable on a rod projecting from the top 
of the field magnets the centre of gravity of the machine was 
adjusted. 

When the machine was carried only on ball-bearings it was 
not sufficiently sensitive, and Dr. Drysdale found that tests 

* See Electrician, p. 517, Vol. LXV., July 8, 1910; Drysdale, Engineering 
November 24, 1905. 


222 


DYNAMOMETERS 


could not be accurately made much within 5 per cent. In 
order that the sensitiveness should be increased, the machine 
was swung on knife edges. Finally, the machine was carried 
by means of a scale-beam placed above it supporting its weight 
through links on each side of it, each joint being of the knife- 
edge and flat kind. By means of the beam and links the 
weight of the machine was taken off the ball-bearings. The 
fulcrum of the beam was adjusted for height by means of a 
vertical screw and wheel. In my own form of balance dynamo¬ 
meter the antifriction wheels were large in comparison with 
the cylindrical bearings of the armature, in some cases as much 
as 10 to 1. For motors which were not very heavy the method 
of support gave good results. 

Marcel Deprez suspended the field magnets of his machines 
of the Gramme type by knife edges on planes outside the 
bearings of the armature which was carried on separate bearings 
on each side of the machine. I have been recently informed 
by Messrs. Joshua Buckton & Co., the well-known makers of 
testing machines, that properly-constructed knife edges and 
planes will carry satisfactorily a load of five tons per inch run, 
the condition for getting a good result being that the highest 
quality of steel be employed, properly hardened, and ground 
dead true so as to ensure a bearing along their whole length. 

Mr. J. Davis and Mr. F. Shaw have employed a cradle dyna¬ 
mometer designed by Mr. A. E. Moore, of the Manchester School 
of Technology, in a research on the output of a generator and 
the efficiency.* Also on the curves connecting iron loss torque 
and speed. This machine is carried on ball-bearings instead 
of knife edges. The results for sensitiveness appear to be 
excellent. 

[A cradle dynamometer is described in the next chapter 
under “ Motor-car Engine Tests,” by Dr. Watson, F.R.S.] 

* The Institution of Electrical Engineers, Manchester, Students’ Section, 
April 19, 1910. 


CHAPTER XIV 


THE DYNAMOMETRIC TESTS OP MOTOR-CAR ENGINES AND HIGH¬ 


SPEED INTERNAL-COMBUSTION ENGINES 

PAGE 

Peculiar difficulties and necessity for flexible couplings .... 223 

Use of calibrated dynamo ......... 224 

“ Milling Machine ” supports ......... 225 

[Instability of speed with friction brakes].226 

[Dr. W. Watson’s investigations] ........ 227 


[Wimperis Accelerometer for brake horse-power tests of motor car engines]. 229 

When an internal combustion engine is tested for brake horse¬ 
power with the usual forms of rope brake, considerable vibration 
is set up and the readings of 
the balance scale are difficult 
to determine with accuracy. 

This arises from the fact that 
the rate of rotation changes 
during each revolution. It 
has been found that the 
vibration can be eliminated 
considerably, when testing 
the internal - combustion 
motor, by connecting it with 
some form of hydraulic brake, 
such as that of Brotherhood. 

The average torque per revo¬ 
lution is then given and a 
trustworthy result obtained. I find when making such a test 
that it is best to connect the motor to the dynamometer through 
two flexible couplings, such as those made under the Zodel- 
Voith patents (Fig. 103). In this coupling each of the two 
opposed flanges, one driving and the other driven, are furnished 
with eight curved projections having rounded ends ; a con¬ 
tinuous belt led to and fro between these projections forms the 
flexible connecting link. Another very early flexible coupling 



224 


DYNAMOMETERS 


consists of a cup-shaped flange connected to a flat flange by 
means of a disc of leather. Another is that used by Messrs. 
Crossley & Co. in connecting their gas engines with a dynamo. 
This consists of two opposed flanges furnished with studs ; the 
flexible link consists of a continuous rope, which is led to and 
fro between the studs alternately. Another simple and 
effective coupling is that of Siemens. The drive is made 
through a spiral spring wound on a shaft, connecting the motor 
and the dynamo. In the Proceedings of the Royal Society of 
Arts, 1910, p. 962, will be found the second Cantor lecture on 
“ The Petrol Engine,” by Prof. W. Watson, F.R.S. The 
indicated horse-power is found by means of the lecturer’s 
excellent device, namely, a corrugated steel diaphragm, cooled 
by water circulating round the chamber in which it is fixed. 
This diaphragm takes the place of the piston of the ordinary 
steam engine indicator. The latter instrument is not suitable 
for very high speed engines owing to the inertia of its piston. 
Prof. Watson’s diaphragm accurately shows the pressures in 
the cylinder when the whole stroke of the piston of the engine 
takes Jo second and the pressure rises to 250 lb. per square inch 
in 0-003 second. By means of two mirrors, one rocked to and 
fro by the diaphragm and another rocked at right angles to it 
by a lever driven from the shaft of the engine, a beam of light 
is given two motions, which when projected on to a screen 
draws an indicator diagram, from which the indicated horse¬ 
power can be deduced. This is photographically recorded. 
The most valuable property of the diagram so found is that it 
shows the relationship of spark ignition to pressure developed. 
But it is with the dynamometric test of the petrol engine that 
we are concerned. 

With some engineers the method of determining the horse¬ 
power by coupling the petrol motor with a calibrated dynamo 
has commended itself. This really means that the dynamo so 
employed gives an electrical output which, when certain 
corrections for losses have been made, exactly represents the 
horse-power employed to drive it. Probably with dynamos of 
considerable size, such as over 50 h.p., no great error would be 
introduced, but with smaller dynamos this is not the case. I 
think that Dr. C. V. Drysdale puts the matter clearly in the 
following paragraph, taken from a paper on “ The Testing of 


DYNAMOMETRIC TESTS OF ENGINES 225 

Electric Generators and Motors,” Engineering , November 24, 
1905 :— 

“ For small machines we are therefore thrown back on the measure¬ 
ment of the input and output. In the case of motors the mechanical 
output may be measured either by a transmission dynamometer or 
brake, while for generators the transmission dynamometer is alone 
available. There is, of course, the option of a ‘ calibrated ’ generator 
or motor, but this is pure begging of the question, as the calibration of 
this machine must be carried out by a dynamometer or brake, and 
cannot be regarded as constant.” 

I have found that the following method yields good results. 
Let the engine to be tested be Coupled to a dynamo accurately 
balanced about the axis of its armature shaft, carried on anti¬ 
friction wheels, or, as Dr. Drysdale has done, on the arms of a 
balance furnished with knife edges. Then the dynamo is 
employed really as a brake, the current being so employed as 
to set up the required torque between the field magnets and 
the armature. Then, if the torque be known and also the 
revolutions per minute, the brake horse-power is known. I do 
not describe the above as by any means a new method. It was 
employed by me many years ago in the Millard Engineering 
Laboratory, Oxford. I think that Dr. Drysdale’s method 
(which has been described on p. 221) of suspending the electric 
machine is excellent and very sensitive. One of the great 
advantages of this method of testing a prime-mover, in which 
the speed varies slightly in the course of each rotation, is that 
it may be continued over a long time, during which changes in 
advance, etc., of spark and vapour mixture can be made with 
ease. The proportion of the size of the dynamo to the engine 
of course must be considered, so that the dynamo may be well 
able to take the work put into it. The following will be found 
to be a convenient form of adjustable base for carrying many 
kinds of engines and motors. A base table furnished with T 
slots to which the engine may be secured by bolts is capable 
of five motions, three being motions of translation at right 
angles to one another and two of rotation, one about 
a vertical axis, the other about an axis at right angles 
to the line of the axis of the engine shaft, the slides in each 
case being of geometrical construction. A modern milling 


226 


DYNAMOMETERS 


machine has these motions, and the axis of the piece to 
be milled can readily be placed where desired. The design of 
this table was partly due to the late Mr. F. M. Newton, of 
Taunton. In order to make improvements in petrol engines, 
in which there are so many variables, the most careful dynamo¬ 
metric tests should be made in conjunction with the indicator 
diagrams, and expenditure on a complete testing plant should 
not be grudged by those who still desire to make further 
progress in the development of this class of prime mover. 

[The internal-combustion engine, and especially the petrol 
engine, as used in a motor car or flying machine, when tested 
with a dynamometer depending on solid friction such as the 
Prony brake, is subject to special difficulty depending upon 
instability of speed. This type of engine for a considerable 
range of speed, including its useful range, develops an amount 
of work per revolution which varies but little with the speed. 
At extreme low speeds this may fall off in consequence of 
cooling of the hot gases and also if there is leakage, while at 
extreme high speeds it may fall off in consequence of insufficient 
supply of mixture and delay in the development of pressure 
with respect to the position of the piston. It results, therefore, 
that for a considerable range the horse-power is nearly propor¬ 
tional to the speed. In the same way the resistance due to 
solid friction is much the same over a very great range of speed, 
and so the horse-power absorbed will be for any setting of the 
brake very nearly proportional to the speed. If, therefore, an 
engine of this type is tested with a solid friction brake and a 
fair balance between the power and the resistance is obtained 
for some speed, this same balance very nearly will obtain for a 
large range of speed and the engine speed will be difficult to 
maintain. The engine may even run away or stop with small 
variations of power. For this reason it is much more con¬ 
venient to test this type of engine with a dynamometer 
where the resistance is proportional to some higher power 
of the speed than the first, such as that given by fluid 
brakes, whether the fluid be air or water. If the power 
absorbed follows a cubic law, as with the fluid brakes, then 
a very small increase of speed will produce so great an 
increase of resistance that any slight access of power has an 
insignificant effect on the speed, which therefore is stable. 


DYNAMOMETRIC TESTS OF ENGINES 


227 


It has seemed to the writer that the Foucault current type 
of brake, described in Chapter VII., in which the increase of 
resistance with speed is less than it is in fluid friction brakes, 
could have the index of its law increased by 2, or nearly so, by 
including a dynamo in the brake the current from which would 
excite the electromagnets which are used for inducing eddy 
currents. If the magnetising coils were so proportioned that 
these only approached saturation at high speed, then the 
increase of resistance with speed would follow a higher law 
than it does with constant excitation and the stability of speed 
would be improved.] 

[In the Proceedings of the Institution of Automobile Engi¬ 
neers of November, 1912, there is an account by Dr. W. Watson, 
F.R.S., of a carefully-conducted test of a petrol engine in which 
the load was taken up electrically, but instead of depending on 
the rating of the dynamo, a method which was found to be 
troublesome and unsatisfactory, the cradle system was adopted. 
The engine was connected by means of a Zodel-Voith flexible 
coupling to a nine-kilo watt electric motor with separately 
excited field. When this was used as a dynamo the load was 
absorbed in a large air-cooled resistance with step switches, so 
that the load, and therefore the speed, could be adjusted. It 
could also be used as a motor when the power needed to over¬ 
come the friction of the engine was being determined. As 
shown in Figs. 104, 105, the motor was supported by two turned 
cast-iron rings A resting on ball-bearing friction pulleys BB 
made of hard steel. As the cast-iron rings were not hard enough 
bands of spring steel were clipped round them, and these could 
be shifted in position if the bearing parts showed any wear after 
long-continued use. A transverse beam with a scale-pan D at 
each end made it possible to apply any torque to the motor 
magnets in either direction, and an oil dash-pot E was used to 
damp out vibrations. A large part of the weight of the motor 
was taken by a knife edge in the eyebolt at the top. The knife 
edge was carried by a wire attached to one end of a pivoted 
beam, the other end of which carried a counter-weight. With 
this compound support the motor is carried in a state of stable, 
not of neutral, equilibrium. This was convenient, for it was 
only necessary to use multiples of the pound on the scale-pans, 
while fractions were read by pointers moving over the scales F. A 

Q 2 


228 


DYNAMOMETERS 


deflection of 3*6 millimetres from the mean position corresponded 
to a torque of 1 pound-foot. The dynamometer worked so 
steadily that the pointer could be read with an accuracy of one 
or two tenths of a millimetre. I have to thank the author and 



Fig. 104. 




the Institution of Automobile Engineers for permission to use 
the illustration.] 

[In the National Physical Laboratory Report for 1910, there 
is an account of a motor-testing plant in which the absorption 
dynamometer consists of a specially-constructed fifty-kilowatt 
direct-current generator mounted in the manner of the cradle 






































DYNAMOMETRIC TESTS OP ENGINES 229 


dynamometer on knife edges, so that the power absorbed may 
be determined without depending on the calibration of the 
dynamo. A water-cooled friction brake is also provided.] 

The Wimperis Accelerometer. 

[In recent years the development of the accelerometer has 
led to a new and extremely practical and quick method of 
testing the brake horse-power of motor-car engines in position 
in the car and on the road. 

Lanchester’s accelerometer is described in the Proceedings 
of the Institution of Automobile Engineers, 1909—10, Vol. IV., 
while that of Wimperis will be found in the Proceedings of the 
same Institution for the year 1914.* As the Wimperis 
accelerometer is the one best suited for this kind of test, I 
shall describe the construction of this one by the aid of 
Figs. 106—108, for which I am indebted to the manufacturers, 
Messrs. Elliot Brothers. 

A and B are two discs geared together and delicately pivoted 
like wheels in a watch. The circle in each represents a hole 
which puts them out of balance. It will be seen that these 
holes are symmetrically placed with respect to the horizontal 
line, and, owing to the gearing, they must always be so. Now 
suppose the instrument in which the discs are pivoted to be 
given an acceleration in the direction of the arrow P, then, 
owing to the want of balance of the discs, the heavy side of 
each will have an inclination to remain behind or the holes 
will tend to move ahead. They will tend to turn in opposite 
directions, and the gearing agrees with this. If one is con¬ 
trolled by a hair-spring like the balance-wheel of a watch, it 
will turn so far that the combined torque due to the two 
unbalanced discs will be equal and opposite to that exerted 
by the spring. If, however, any acceleration is applied in the 
direction of the arrow Q, the tendency of the two discs will be 
equal and in the same direction of rotation, but as this is 
inconsistent with the gearing this acceleration has no ultimate 
effect. Similarly, acceleration perpendicular to the plane of 
the paper can have no effect either. 

* See also British Association Report, 1910; Proceedings of the Institution of 
Civil Engineers, Vol. CLXXXVIIL, and “The Principles of the Application of 
Power to Road Transport,” by H. E. Wimperis. London. Constable and Co., 
Ltd., 1913 


230 


DYNAMOMETERS 


It will be clear, then, that such a construction picks out 
acceleration in the direction of the arrow P, or retardation 
which is negative acceleration, and responds to it, but 




is insensible to acceleration in any direction perpendi¬ 
cular to this. The left hand side of Fig. 106 is a 
plan diagram of the construction of the instrument. Here 
the two spur-wheels are seen geared together. The upper 
one carries a larger copper disc in which the unbalancing 








DYNAMOMETRIC TESTS OF ENGINES 


231 


hole is made. The lower one carries a hand which moves over 
the dial seen in Fig. 107. The positive weight of the hand is 
dynamically equivalent to the negative weight of a hole on the 
other side of the centre. The hair-spring is so attached as to 
make the pointer lie over the zero of the acceleration scale 
when the instrument is level and at rest and then the angles 
a, )8 are then each of them 180 degrees. With accelera¬ 
tion the pointer moves to the left, while with retardation it 
moves to the right. As the reaction of the spring is propor- 



Fig. 107. 


tional to the angle of deflection, while the arm at which the 
centres of gravity of the moving elements acts varies as the 
cosine of this angle, the scale of acceleration and retardation is 
not one of equal parts, but one based on the cosine law. The 
copper disc moves between the poles of the magnet as 
shown, thus experiencing a force of retardation proportional 
to its velocity, and so vibrations are damped out and steady 
readings obtained. The instrument stands upon three feet, 
the one in the direction of travel being furnished with a levelling 
screw to bring the pointer to zero when all is quiet. 

Acceleration is literally the rate at which velocity changes, 
and it is measured as velocity per second or feet per second 




232 


DYNAMOMETERS 


per second added or subtracted. As the action of force upon 
mass is to produce acceleration, the term “ acceleration ” is 
often used, conveniently but wrongly, as though it were force. 
In dynamical units the acceleration due to gravity is 32*2 feet 
per second per second, while the acceleration due to diluted 
gravity down a frictionless incline of 1 in 10 is 3*22 feet per second 
per second. 

It is often convenient where acceleration is measured with a 
view to determine forces to reckon the force as so many pounds 



per ton of the weight of the car being examined. Thus, if the 
acceleration of the car is 1 foot per second per second, this 

acceleration would be caused by —of its weight, or by a force 

32*2 


measured in gravitational units as 


2,240 

32-2 


69*6 pounds per 


ton in excess of that needed to overcome resistance to steadv 
motion. The number 70 is so near 69*6 that it is commonly 
taken as the number of pounds per ton corresponding to unit 
acceleration—or retardation if the action of a brake is being 
considered. 

If an accelerometer is placed upon the floor of a car and care- 












DYNAMOMETRIC TESTS OF ENGINES 


233 


fully levelled when the passengers are in their places, and then 
the car is started on a level road in the usual way, the needle of 
the instrument will show the acceleration through all the 
operations of letting in the clutch, and during the steady 
increase of speed on each gear, dropping for a moment to a 
negative quantity as the gears are being changed. Two examples 
taken with a recording accelerometer are shown in Fig. 108. 
These were taken on a three-speed touring car at Brooklands. 
The upper curve shows the acceleration when speed was got 
up as quickly as possible, while when the lower one was 
obtained this process was not unduly hurried. The greatest 
acceleration is due to the coming into action of the clutch, and 
the next is got with the low gear. It is the drop of accelera¬ 
tion to a negative quantity with which we are immediately 
concerned. 

Taking a car first on a level road and driven at any desired 
speed, the speed must first be read on a speedometer, and then 
when all is going steadily the clutch is suddenly thrown out of 
action and the accelerometer read. The car meets with resistance 
due to road friction, to internal friction in the mechanism 
between the road wheels and the clutch, and to wind or air 
resistance, and this last at high speeds is the most important. 
In virtue of these resistances its acceleration, which was zero 
when it was moving at a uniform speed, becomes suddenly 
negative, and this may be read as so many pounds per ton. 
Up to the moment of declutching, when the velocity was 
uniform and the acceleration zero, the engine was providing 
the power to overcome these resistances, i.e., it was applying a 
force of the ascertained number of pounds at the speed of the 
car. The following example is taken from the makers’ 
pamphlet :— 

Weight = 1*67 tons 

Tractive resistance by accelerometer =165 pounds per ton = 
275-5 pounds. 

Speed = 44-78 miles per hour = 65-7 feet per second 

275-5 X 65-7 , 

Brake horse-power =--== 32-9, or 33 as nearly as 

it can be ascertained ; 

W X R X V , , , 

or, more shortly,-^-= brake horse-power, 




234 


DYNAMOMETERS 


where W = weight in tons 

R — tractive resistance in pounds per ton 
and V = velocity in miles per hour. 

The following values have been found for R :— 

Clean wood or hard macadam . . 70 lb. per ton. 

Muddy and sticky road . . . 95 „ „ 

Road metal partly rolled . . 120 „ „ 

Loose road metal not rolled . . 200 „ ,, 

So far we have been considering a level road only. If the road 
is not level, the real acceleration of the car in feet per second per 
second will be altogether different ; nevertheless the readings 
of the accelerometer as indicating forces applied by engine or 
by brake will be true, and for this purpose the slope of the road 
has no effect. This is a surprising result to many, but a 
moment’s consideration will show that, in so far as the actual 
movements of the car are affected by the slope tending to move 
the accelerometer needle in one direction, the consequent slope 
of the instrument will act to an equal extent in the opposite 
direction. That this must be so is most readily proved by 
considering a model cart moving without friction down an 
inclined plane. If such a cart were to carry a pendulum, the 
pendulum would lean forwards relatively to the cart if this 
were at rest, but if it were liberated and were free to accelerate 
under gravity, meeting with no friction on the plane, the 
reaction between the plane and the cart and all its contents 
would be perpendicular to the plane and the pendulum would 
hang square to the cart, the same as if they were on the level 
and at rest. The pendulum is an accelerometer of simple 
construction, and so the reading on an incline with no forces 
acting except gravity is zero. As the accelerometer acts 
dynamically as a pendulum in relation to fore and aft motion 
and acceleration, it also is its equivalent as an indicator of 
slope. The scale of the instrument is therefore provided with 
a lower set of divisions which will indicate by the position of the 
pointer the gradient on which the car is standing or on which 
it is moving, provided that the speed is uniform or the accelera¬ 
tion zero. It should be pointed out that there is one error in 
the statement as to horse-power as made. The weight of the 
car in tons should have a very small amount added to it 
corresponding with the rotational energy of the road wheels 


DYNAMOMETRIC TESTS OP ENGINES 235 


and revolving mechanism up to the clutch. The tyres, for 
instance, should be counted nearly twice over, and the other 
parts in a proportion less than this. If W is taken to mean 
the weight in tons increased in this way by the right amount, 
then the expression given is correct. 

It may be well to add the statement that in the instruments 
as at present made the large amount of dead and useless 
material of the unbalanced discs is no longer employed, but 
instead the same departure from balance is obtained by the 
use of a short light arm with a small weight at the end.] 


CHAPTER XV 


SHIP MODEL DYNAMOMETER 

PAGE 

Froude’s original researches ......... 236 

Admiralty tank and equipment at Haslar . . . . . .238 

List of other tanks .......... 245 

The very important researches of William Froude, made at 
Torquay, on the friction experienced by ships moving through 
water have borne an excellent harvest, and an experimental 
plant very similar to Froude’s original one at Torquay was 
erected by the Admiralty at Haslar, where excellent and 
constant work is carried on by his son, R. E. Froude, F.R.S. 

The importance of the work has been thoroughly recognised 
by foreign Powers and private shipbuilding firms. In order 
that the behaviour of a model of a ship may be compared with 
the behaviour of the ship itself, Froude employed a “ scale of 
comparison,” as he called it ; this was based on the stream line 
theory, and is thus stated :— 

“ If the ship be D times the dimension of the model, and if 
at speeds V x , V 2 , V 3 the measured resistances of the model are 
R l5 R 2 , R 3 , then for speeds VjVD, V 2 Vd, V 3 Vl) of the ship, 
the resistance will be D 3 Rj, I) 3 R 2 , D 3 R 3 . . . Froude applied 
the expression “ corresponding speeds ” to the speeds of the 
model and ship. An example taken from Froude’s paper in 
Vol. XV. of the Transactions of the Institution of Naval 
Architects, and quoted by Sir William White, “ Manual of Naval 
Architecture,” 1894, p. 478, will make this clear. 

In Fig. 109 is shown a “ curve of resistance,” in which 
abscissae represent speed in feet per minute, set off along XY, 
while the ordinates represent the resistance of a ship or a model 
of a ship in pounds at different speeds. By means of a traction 
dynamometer, which will be described later on, the resistance 
of a model, say, at 240 ft. per minute is found ; this value is set 


SHIP MODEL DYNAMOMETER 


237 


off as an ordinate, ad, at the point d, which corresponds to the 
speed. Several points, such as a, are found for different 
speeds, and through these the curve A A is drawn. From a 
curve so formed the resistance can be found for any speed 
included in the experiments. From the immersed surface of 
the model and an experimental determination of the coefficient 
of friction the frictional resistance for each speed can be 
calculated. 

Next the frictional resistance is set off from the base line XY 
for each speed on the same scale. For a speed 240 ft. per 
minute db represents the frictional resistance. Thus a curve 
BB of frictional resistance is found for the model. From these 



data the resistance of the full-sized ship can be found. . Froude 
made his experiments on the Greyhound ; the scale of the model 
was one-sixteenth that of the ship : so that for the scale of 
comparison D = 16 : a/D = 4 ; and therefore the “ corre¬ 
sponding speeds ” of the ship will be four times those of the 
model. In the figure the speeds for the model are marked 
below XY ; and the speeds of the ship above this line Then 
Resistance of ship = (16) 3 X resistance of model. 

- 4,096 X 

This change, therefore, simply amounts to an alteration in the 
scale of measurement of the ordinates of the curve AA ; and what¬ 
ever length represents 1 pound for the model must represent 
4,096 pounds for the ship. On the right of the curve diagram the 
correction is shown by the scale of “ resistance of ship ”—in 






















238 


DYNAMOMETERS 


fresh and in salt water. This scale gives values for resistance 
in fresh water and sea water, the resistance in salt water 
exceeding that in fresh water in the ratio of the density of sea 
water to fresh water. The scale was employed since in the 
experimental tank fresh water was used. Since the length of 
the ship greatly exceeds that of the model a correction is 
required on this account. The frictional resistance of the ship 
is calculated for the various speeds, her actual coefficient of 
friction being made use of, and these are set off, on the proper 
scale and on ordinates representing the corresponding speeds, 
downwards from the curve BB, which represents the frictional 
resistance of the model ; through the points then determined 
the curve CC is drawn. Then, to determine the resistance of 
the ship at any speed instead of measuring from the base¬ 
line XY, it is necessary to measure from the line CC. I am 
indebted to Sir William White, F.R.S., for his kind permission 
to reproduce the figures and description from his “ Manual of 
Naval Architecture,” p. 479. 

The mechanical problem which William Froude set himself 
to solve was to make exact models of full-sized ships and then 
to tow them through water at a uniform known velocity. The 
force required to tow them was accurately recorded during the 
whole transit of the models. The exhaustive paper of William 
Froude, F.R.S., in Vol. XV. of the Transactions of the Institu¬ 
tion of Naval Architects, and that of his son, R. E. Froude, 
F.R.S. (Institution of Mechanical Engineers, February 2, 
1893), should be carefully read by any one wishing to appreciate 
the material outcome of genius and ability. Only enough will 
be stated here by way of an outline of this splendid piece of 
work. 

The different parts of the model ship-testing apparatus are 
these :—The water way ; the experimental carriage ; the 
engine and hawling gear ; the governor of the engine ; the 
model-shaping machine ; the copying apparatus ; the forming 
of the model; the weighing of the model; the record of an 
experiment. 

The water way is in the form of a canal. At the 
Admiralty Experimental Works, Haslar, it is about 400 feet 
long, of nearly uniform section, having vertical sides. On 
each side of this tank rails are laid down, and on these, which 


SHIP MODEL DYNAMOMETER 


239 


are nearly 21 feet apart, the experimental carriage runs. In 
the first ship model apparatus the experimental carriage was 
carried from the roof built over the tank, which was constructed 
at Torquay by William Froude. The experimental carriage is 
equipped with recording dynamometric apparatus, so that the 
pull is recorded by means of a pen on a sheet of paper which 
covers a cylinder, driven from one of the flanged wheels of the 
carriage ; on the same paper a simultaneous record is made 
by a pen actuated by an electromagnet, the circuit of which is 
broken by a clock at definite intervals ; another pen records 
a broken fine showing distances passed by the carriage. 
The ordinate of the diagram produced is directly proportional 
to the force of traction at any instant. The carriage is of 
peculiar construction ; the members of the trusses of which it 
consists are formed out of wood, in the form of trunks or boxes 
about 4 inches square in cross-section, the sides being -| inch deal 
put together with shellac varnish and screwed. The strength 
of this structure for its weight is very great, and it has stood the 
test of many years of constant work. Sir William White when 
commenting on the construction said : “It was indeed an 
admirable example of structural arrangement with so light a 
material, which had not been supposed to lend itself to the 
girder method of construction.”* The carriage is shown in 
Fig. 110. 

The carriage is propelled by means of a wire rope, led over a 
grooved sheave, driven by a 10-inch Tower spherical engine. 
The range of speed for towing the carriage is between 100 and 
500 feet per minute, and a speed as high as 1,200 feet per minute 
has been reached. The governor is quite different from all 
other centrifugal governors. The centrifugal force due to two 
masses of metal is opposed by a spiral spring ; when the ad¬ 
justed distance is reached by the masses they cause a disc, 
sliding on the spindle of the governor, to engage frictionally 
with a disc, to which a link is attached which actuates the 
supply valve of the engine. This is slightly rotated and the 
supply of steam lessened. The performance of this governor 
is excellent and reliable. A similar principle is embodied in 
the driving mechanism of one form of the phonograph. In 

* Proceedings of the Institution of Mechanical Engineers, February 2, 1893, 


240 


DYNAMOMETERS 


this case clock-work drives the phonograph by frictional 
engagement through a minute centrifugal governor only when 
the desired speed is not exceeded, and thus the recording 
cylinder is driven at a uniform speed. 

The model ships are made of hard paraffin wax about 14 feet 
long, and when finished about 1 inch in thickness, an allowance 
of \ inch being made for finishing them accurately to shape, 
which is effected by a model-shaping machine (Figs. Ill and 
112). Fig. 112, which is a transverse section, is on a larger 
scale. This machine consists of the model table, which has a 
maximum travel of 20 feet, on which the cast model is fixed keel 
upwards. On each side of the model two fly-cutters revolve at 
2,700 revolutions per minute ; while the unshaped cast model 
traverses between these cutters they are caused to follow the 
lines of the ship, drawn on paper, so that contour lines are cut 
on the model. After a sufficient number of these have been 
cut the model is removed, and the surface finished by tools of 
the spoke-shave type in such a way that all the contour lines 
cut by the fly-cutters are joined. The movements of the table, 
with the model on it, and the copying point are all under the 
control of the operator. The table is traversed by means of a 
piston moving in a long cylinder, the piston-rod being a 
continuous steel piano wire, led out through glands at each 
end of the cylinder and then over pulleys. The piston is moved 
by oil under a pressure of 14 pounds per square inch, pumped by 
a small vane pump. This machine should be seen to appreciate 
its numerous points of excellence. The models are cast in 
moulds made of white clay contained in a long rectangular box. 
The melted wax is used at a temperature of about 160° F. 
After the model ship is finished it is weighed, so that correct 
additional weights may be put into it to give it the right depth 
of flotation. In order that the behaviour of the model ship 
may give results from which the behaviour of the full-sized 
ship may be truly predicted, every measurement connected 
with the model ship must be as accurate as possible ; this 
accuracy has been attained in a high degree in the testing 
plant at Haslar. Many other points are also investigated, such 
as screw efficiency and the effects due to wave-making. 

Referring again to Figs. Ill, 112, V is the traversing 
carriage with the paraffin model on it, being shaped by th^ 


SHIP MODEL DYNAMOMETER 


241 



g 

£ 


revolving cutters, carried on the spindles RR. AA are 
wheels for raising the cutters symmetrically. These are 
rotated by the gearing B and cross-shaft DD, on which slides 
d. k 


















































































































242 


DYNAMOMETERS 



the spur wheel B, fitted with a sliding feather. The rotation 
of D is effected by the hand-wheel Q through mitre gear ; the 
hand-wheel Q also moves the indicating nut F through the 


Fig. Ill 






















































































SHIP MODEL DYNAMOMETER 


243 



h 2 


Fig. 112. 
























































































244 


DYNAMOMETERS 


distance of the vertical rise or fall of the cutters, so that they 
can be set by this means at the levels of the successive water 
lines marked on G. The lateral motion of the cutters, which is 
symmetrical, is controlled by a right and left handed screw H, 
engaging in the nuts SS. This is worked by mitre gear through 
the hand-wheel U. The cutters always work from midships of 
the model towards its ends, so that they continuously move 
inwards ; their sliding friction is reduced by the counter¬ 
balance levers and weights WW. The fulcrum M of the 
copying lever J (indicated by a single line) is mounted on the 
frame K, which is also a lever pivoted at L, just beneath the 
line of motion of the cutter end of the copying lever, being held 
at the other end at the point I, in the line of motion of the 
tracer, by the frame N. The position of N in the direction of 
the travel of the tracer is regulated by the roller Y, held in 
contact with the back edge of the batten P by means of a light 
weight over a pulley, the front edge of the batten being adjusted 
to a uniform distance from the centre line of the drawing. 
The proportional longitudinal travel of the drawing fixed to 
the table to that of the model is regulated by the change 
wheels X, the teeth of the cog-wheels being always kept in 
contact by a weight acting through a line over a pulley ; thus 
any play of teeth is avoided. The motion of the table carrying 
the model is given to it by a piston and cylinder actuated by 
oil, pumped by a small centrifugal pump Z (this has been 
previously described). The tracer is not a point but a circle of 
the same diameter as the cutters, and its edge is kept in 
contact with the lines of the drawing while the cutting is made ; 
if the plan and model differ in length, then in place of a circle 
an ellipse is used, the axes being proportional to the relative 
length of the plan and the model. No difficulty is experienced 
in keeping the edge of the circle or the ellipse in contact with 
the lines of the drawing, or in manipulating the hand-wheels 
and foot-gear, which are all in easy reach of the operator. 

The example set by the British Admiralty has been followed 
by several foreign Governments—France, Italy, Germany, 
Russia, and Japan. Also some shipbuilding firms have added 
a complete model-testing plant to their works : the pioneers 
in this are Messrs. William Denny & Sons. Quite recently a 
testing tank for ship models has been built at the National 


SHIP MODEL DYNAMOMETER 


245 


Physical Laboratory, Teddington, where every detail has been, 
thought out with great care, much being due to Mr. Horace 
Darwin, F.R.S. It was initiated by the Institution of Naval 
Architects, Mr. A. F. Yarrow offering, subject to certain con¬ 
ditions, the sum of £20,000 to defray the cost of its construc¬ 
tion and its outfit (Report of the Experimental Tank 
Committee (1908), Institution of Naval Architects). 

Instead of the towing engine of Froude an electrically-driven 
motor is employed. This motor forms part of the experimental 
carriage, so that any vibration due to a long steel-rope drive is 
obviated. When we consider the enormous tonnage of the 
war and mercantile shipping belonging to England, the great 
importance of such a plant, where different naval architects 
can obtain trustworthy and careful tests of their designs, 
cannot be over-estimated. 

Notes on Experimental Tanks. 

Chronological order of eight Experimental Tanks :— 


Torquay, first of such tanks . 

. 1872 

Dumbarton, Messrs. Denny & Sons 

. 1882 

Admiralty Tank, Haslar 

. 1886 

Spezia tank ..... 

1889 

Washington tank .... 

1898 

Bremerhaven tank 

1900 

Berlin tanks..... 

. 1902 

Uebigau tank .... 

. 1904 

National Physical Laboratory 

. 1910 

Tank in construction. 



[The National Physical Laboratory tank and equipment at 
Bushey have been completed since the author wrote his account 
of Froude’s work. As the general design is based upon that of 
Froude, though in detail there are alterations and improve¬ 
ments, and electric motors in particular have facilitated the 
operations, it seems unnecessary to describe these in detail. 
It is sufficient to refer to the collected researches of the National 
Physical Laboratory, Vols. VI. to IX., or to the Transactions 
of the Institution of Naval Architects of 1910 and succeeding 
years.] 





246 


DYNAMOMETERS 



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CHAPTER XVI 


THE AERONAUTIC DYNAMOMETER 

PAGE 

National Physical Laboratory apparatus ...... 247 

Viokers, Sons and Maxim’s apparatus ....... 249 

Through the courtesy of the secretary of the Advisory 
Committee for Aeronautics, 1910, I am able to give a descrip¬ 
tion, with figures, of the dynamometer used in experiments 
made on air propellers. Problems in air resistance have long- 
ago been studied by employing some kind of whirling table, 
that is an arm, revolving in a horizontal plane, carrying the 
surface opposed to air friction and pressure at its end. This 
method was employed by Robins in 1746, Hutton in 1787, 
Smeaton in 1759, Hirn in 1854, also more recently by Dines in 
England and Langley in America. When an arm of great 
length is employed as the carrier of the surface or propeller, a 
close approximation to the conditions existing in an actual air 
machine can be obtained. The radius of the arm of the whirling 
table at the National Physical Laboratory is 30 feet; it rotates 
within a galvanised iron shed 80 feet by 80 feer, so as to be 
free from atmospheric disturbance. 

The 30 foot arm is built up of light steel tubes tapering 
from lj inch diameter at the axis to 1 inch at the extremity ; 
they are 12 \ inches apart, and are connected together by struts 
(Figs. 113, 114 and 115). The central post rises 6 feet above 
the tubes, and the stiffening is effected by connecting the tubes 
to a cantilever built up of light angled irons furnished with 
cross-bars and steel-wire ties. A 14 horse-power electric 
motor drives the arm through worm-wheel reduction gear of 
28 to 1. 

In order to prevent the post being strained by the inertia of 
the arm when stopped, the post is divided above the worm- 
wheel, the upper and lower parts being connected by a ratchet 
gear which allows the full rotation of the arm when the motor 


248 


DYNAMOMETERS 


is stopped. The arm can be driven from five to thirty revolu¬ 
tions per minute ; this corresponds to a speed of the propeller¬ 
testing mechanism of from ten to sixty miles per hour. Current 
is supplied to the testing mechanism through slip-rings fixed 
to the central post, and wires connecting them with the motor, 
etc. The propeller shaft is driven by a half horse-power motor, 
carried by the arm 8 feet from its extremity, the motion being 
given to the shaft by a belt. This motor is furnished with a 
speed-regulator worked from the observing table, so that when 
an experiment is being made both the speed of rotation of the 
propeller and its forward movement can be separately con¬ 
trolled. 

The propeller dynamometer is shown in Figs. 116 and 117 ; 
it is so designed that the torque on the propeller shaft, due to 
a given thrust, is recorded on a drum. To effect this the ball¬ 
bearings carrying the propeller shaft are supported by a link 
motion which allows a small horizontal movement of the shaft, 
this motion being controlled by the spring S x . The pulley P, 
by which the shaft is driven, is mounted on the bracket B, and 
transmits motion to the shaft through the outer casing of the 
oil dash-pot DP and the coiled spring S 2 . On the face of the 
casing of the dash-pot a lever is carried ; this is furnished with 
a pencil, which can scribe a line on paper on the drum attached 
to the propeller shaft. The end of the propeller shaft is 
connected to the armature of a small generator G, so that the 
speed of rotation can be found from the readings of a voltmeter 
on the observing table. In making an experiment on a pro¬ 
peller the tension of the spring 8 1 is set to a given value and the 
speed of the whirling kept constant. The speed of the propeller 
shaft is gradually increased by means of a regulator until the 
thrust of the propeller is sufficient to balance the pull of the 
spring. When this balance has been effected the propeller 
shaft moves back on the link motion through a small distance. 
This is recorded by a movement of the pencil parallel with the 
axis of the propeller shaft. The trace thus made on the drum, 
which shows the circumferential motion of the pencil, is read 
and the torque corresponding to a given thrust deduced. In 
order that the desired thrust may be known the lever of the 
link motion by means of contacts shows either a red or a green 
light on the whirling table. 



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THE AERONAUTIC DYNAMOMETER 


249 


Air-propeller Testing Plant at Messrs. Vickers, Sons 
and Maxim’s Works, Barrow in Furness. 

This apparatus consists, as will be seen from Figs. 118 and 
119, of a steel cantilever, accurately balanced and suspended in 
such a manner that it is free to revolve about the head of a 
cast-iron column. The point to which the suspension rods 
converge is a steel bracket to which is fastened a steel tube, 
constructed of rolled-steel plates, but jointed and riveted. At 
the head of this tube there is a ball-bearing which supports the 
entire weight of the moving portion of the structure, a guide 
from the bottom end being supplied by four horizontal rollers 
carried on cast-iron brackets bolted to the lower end of the 
steel tube and rolling on a turned belt on the column. 

The arm which revolves is built up of steel angles, and is 
provided with a covered-in observation station at the centre, 
which contains the 100 horse-power motor and the recording in¬ 
struments. At the extreme end of the arm, and 110 feet from 
the centre, there is a steel platform carrying the bracket and 
bevel gearing for driving the propeller, the power being trans¬ 
mitted along the arm by a line of steel shafting. The other 
end of the arm terminates in a sheet iron ballast tank at a 
radius of 56 feet, by means of which it is possible to balance 
the whole structure. 

The revolutions of the propeller may be varied from 500 to 
over 1,000 revolutions per minute. The speed of the propeller 
through the air can be regulated by means of screens, so as to 
conform to the conditions for which it is designed, which speed 
may reach seventy miles an hour. 

A system of accurately measuring the thrust of the propeller 
is included in the design of the bracket and gearing, the pro¬ 
peller shaft being allowed to move forward against a spring, 
which movement is mechanically recorded in the observation 
station. Experience shows that the thrust can be accurately 
measured to within 1 per cent, in a total thrust of 500 pounds. 

The gear is made with a reverse so that the efficiency of the 
propellers can also be tested for going astern. 

The whole of the conditions for this machine are exactly 
similar to those of a ship running in a straight line through the 
air, as an ingenious method for compensating for the circular 


250 


DYNAMOMETERS 



Fig. 118. 







THE AERONAUTIC DYNAMOMETER 


251 


motion of the propeller has been arrived at, without which, in 
similar machines, that portion of the propeller blade nearest 



the centre column is caused to travel less rapidly than the outer 
portion. 

Provision has also been made for attaching a gondola to the 


Fig. 119. 










252 


DYNAMOMETERS 


platform ahead of the propeller, so that the results obtained 
from the machine may be relied upon as being exactly similar 
to those which will actually prevail when the propeller is placed 
on the ship, astern of the gondola. By this means the exact 
condition of the propeller when it is thus fitted in position in 
the ship may be imitated. 


INDEX 


Abakan ovicz, Abdank, principle of his integraph, 61 
Absorption brake dynamometers described, 91—93 
Acceleration, principle of the Wimperis accelerometer explained, 229— 
235 

Aeronautic dynamometer, apparatus described, 247—252 
Air, 

density : effect on air brake experiments, 116—117 
movements studied by means of chromophotography, 135—136 
Air brakes, 

laws established experimentally, 114—117 
logarithmic chart of horse-powers, 117—119 
observations on, 119—120 
Walker, 113—114 

White and Poppe, and formula, 117—118 
Air propellers, experiments, 7, 247—252 
Alden absorption dynamometer, 93 
Amsler, Dr. Alfred, 

torsion dynamometers, 215—216 
transmission dynamometers, 181—182 
Amsler-Laffon, Prof., planimeter, 51—57 

Amsler polar planimeter, description and explanation, 51—57 
Angle of torsion. See Torsion, Angle of. 

Appold and Amos, friction brake, 89 
Arago, electrical experiments, 121 

Area method, earliest application of, for finding the product of force 
and space, 44 

Area of a figure, methods of finding, 49—50, 53 
Ashton and Storey, continuous steam engine indicator, 46 
Atkinson gas engine, trial by Society of Arts, 76 
Atwood, G., F.P.S., illustration of Smeaton’s work-measuring instru¬ 
ment, 7 

Automatic friction machine, for finding coefficient of friction of a 
band on a pulley or wheel, 32—38 
Ayrton, Prof., formula for frictional hold, 84 
Ayrton and Perry, 
band brake, 75 

transmission dynamometer, 173 

Babbage, Charles, electrical experiments, 121 
Balk, brake dynamometer of, 90 


254 


INDEX 


Ball, Prof., on the Amsler planimeter, 50 
Ball, Sir Robert, F.R.S., 

. assistance to author acknowledged, 15, 23 
on laws of friction, 25 
Band machine, for measuring work, 13—14 
Beaumont, W. Worby, M.I.C.E., 

assistance to author acknowledged, 15 
paper on dynamometers, 4, 83 
Berlin, ship model testing tank, 245, 246 

Bernouilli, J., re-invention of method of winding up weights by ropes, 

71 

Bernoulli, Daniel, opinion on mechanical work of men proved inaccu¬ 
rate, 132 

Block brake dynamometers, described, 86—93 
Blohm and Yoss, of Hamburg, 

assistance to author acknowledged, 15 
investigation of torsional stresses on propeller shafts, 206 
Bochumer Verein, torsion test of propeller shaft, 208 
Bollard friction, 

property of coiled rope explained, 68—69 
use of, in drawing wire, 39 
Borda, M. le Chevalier de, 

experiments on hydraulic wheels, 7 
on the flow of fluids from orifices in vessels, 133—135 
Bosanquet, Mr., apparatus for reading speed of shaft, 172—173 
Boswell, Mr., re-invention of method of winding up weights by rope, 71 
Boulogne, M., re-invention of method of winding up weights by rope, 
71 

Boulton and Watt, early estimates of force of steam engines, 8—9 
Bourdon end thrust brake, 125 
Bourry, M., dynamometer, 176 
Boys, C.Y., 

papers on integration, 50 

transmission dynamometer described by, 175—176 
Boys’s engine power meter, explanation of, 61—64 
Brackett, Prof. C. F., cradle dynamometer, 220 
Brakes, 

air, 113—120 

block brake dynamometers, 86—93 
end thrust, 125—127 
friction, 67—94 
water, 95—112, 223 
Bramwell, Sir Frederick, 

on principle of water brake, 105 
paper on Amsler’s planimeter, 50 
Bremerhaven, ship model testing tank, 245, 246 
Broughton, H. H., torsion dynamometers, 216—217 
Browett, Lindley & Co., dynamometer on Froude principle used for 
steam engine, 105 


iNDEX 


255 


Brown, S. G., 

absence of lateral friction made use of in cable relay, 42 
principle of mechanical relay used, 40 
Buckton, Joshua, & Co., on knife-edge suspension, 222 
Bushey, ship model testing tank, 4, 245 


Cable, British Atlantic, rope brake of William Thomson invented in 
connection with laying pf, 75 

Cable, French Atlantic, friction brake designed for controlling pay 
out, 89 

Calibration of dynamometers, methods described, 168, 171—173 
Carpentier, brake dynamometer, 85—86 
Central Technical College, London, rope brakes at, 78—80 
Chauvenet, method of least squares, 21 

Chromophotography, movement of air studied by means of, 135—136 
Chronometric motor, dynamometer of Morin, 157—158 
Churchward, G. J., assistance to author acknowledged, 15 
Clydebank, ship model testing tank, 246 

Coignet, Captain, method of utilising man’s labour at Vincennes, 11 
Coiled ropes, 

early applications of, 67—68 
resistance of, on a cylinder, 68—69 
See also Rope Brakes. 

Coope, Mr., block brake dynamometer, 88—89 
Cooper’s Hill College, friction brake used at, 80—82 
Cotterill, Prof. J. H., method of showing value of friction of a 
band on a cylinder, 28—30 

Coulomb, C., method of utilising men’s labour, 10—11, 128—131 
Couplings, flexible, necessity for in testing internal combustion 
engines, 223 

Cradle dynamometers, 218—222, 227—228 

Critical velocity, investigations by Prof. O. Reynolds, 142—143 
Croft, W. B., Physical Laboratory of Winchester College organised 
by, 31 

Crossley, Messrs. L., of Halifax, ergometers used, 60—61 
Crossley & Co., flexible couplings used, 224 
Crossley gas engine, trial by Society of Arts, 76 

Current growth, principle of Froude’s turbine dynamometer explained, 
102—103, 108 


Dalby, Prof. W. E., 

dynamometer of, 180—181 
on draw-bar dynamometers, 189 
Dana, R. W., assistance to author acknowledged, 16 
Darwin, Horace, F.R.S., work on testing tank for ship models at 
Teddington, 245 

Davis, J., employment of cradle dynamometer, 222 
Denison balance used in water brake, 111 


250 


INDEX 


Denny, Archibald, 

assistance to author acknowledged, 15 

diagrammatic registration of power used in torsion meter, 47 
experiments on electrical method of reading the torsional angle, 
203—206, 212 

on necessity for torsion meters, 190 
Denny, William, & Sons’ ship model testing tank, 244, 245, 246 
Denny-Johnson torsion meter, 212 
Density of air, air brake experiments, 116—117 
Deprea, Marcel, knife edge suspension used by, 222 
Differential gear, use of, in torsion meters, 195—196 
Dines, Mr., method of studying air resistance, 247 
Dolfus Mi eg, of Mulhouse, dynamometer of M. Matter used by, 174 
Draw-bar dynamometers, 189 
Drysdale, Dr., 

cradle dynamometer, 220—222, 225 

on testing electric motors by a calibrated dynamo, 224—225 
Duckitt, J\, assistance to author acknowledged, 16 
Dynamic weighing by taring, method described, 171—173 
Dynamometers, 

absorption of energy in generating electric currents, Foucault 
type, 121—124 

adoption of word unfortunate, 4 

aeronautic, 247—252 

air brakes, 113—120 

block brake, 86—93 

Boys’s engine power meter, 61—64 

cradle, 218—222, 227—228 

division into three classes, 5 

draw-bar, 189 

friction, 17—43 

friction brake, 67—94 

gravity form, method explained, 5—15 

importance of, 3—4, 107 

mechanical integrator used in connection with, 58—61 
planimeters, 44—66 

recording apparatus used in conjunction with, 45—66, 106 
ship model, 236—246 ; record taken during testing, 64—66 
torsion meters, 190—194, 195—217 
transmission, 144—189 
water brakes, 95—112 
Dynamometric tests, 

calibrated dynamo for, objection to, 224—225 

high-speed internal combustion engines, of, 223—235 

history of methods employed, 1—3 

importance of, 3—4, 107 

motor car engines, of, 223—235 

Society of Arts, 76—77 

Wimperis accelerometer described, 229—235 


INDEX 


257 


East London Technical College, Thurston torsion meter made for, 217 
Easton and Anderson, transmission dynamometer, 161—162 
Eddy current testing brake of Morris and Lister, 122—124 
Eddy motion, cause of resistance of ships, 140—141 
Edgecombe, Mr., diagrammatic registration of power used in torsion 
meter, 47 

Edgeworth, R. L., F.R.S., method for measuring work done by road 
carriages, 9—10 

Electromotors, cradle dynamometers for testing, 218—222 
Elliot Brothers, manufacturers of the Wimperis accelerometer, 229 
End thrust, question of effect on propeller shafts, 214—215 
End thrust brakes, 

Bourdon, 125 
Jervis-Sraith, 125—127 
Engines, 

importance of dynamometric tests, 3— 4, 107 

investigation of torsional stresses on propeller shafts, 206—208 

machines for testing. See Dynamometers. 

testing. See Dynamometric Tests. 

Equiangular spiral. See Logarithmic Spiral. 

Ergometer, 

for account of machines, see Dynamometers. 
use of the term, 5 

Ernst Integrator, method of finding quadrature of the curve by, 151— 

155 

Ersatz Kandor, cruiser, Lux torsion meter used for, 217 

Faraday, Michael, the dynamo the outcome of his experiments, 121 
Farcot, M., dynamometer of, 179 
Farey, John, 

early estimate of horse-power, 8—9 
slide rule invention, 9 

treatise on the steam engine quoted, 44—45 
Fluids, 

flow of, from orifices in vessels, Borda on, 133—135 
solution of problem of resistance of, 134 
Fottinger, Dr., torsion meter, 209—212 
Foucault, Leon, 

brake of, suggestions for modification of, 227 
experiment for estimating the heating effect of eddy currents, 122 
Frahm, Hermann, 

measurement of power absorbed by ship propellers, 47 
torsion meter, 206—208 
Prahm speed indicator, 206 
Friction, 

authorities on, list, 17—18 
automatic friction machine, 32—43 

between a liquid and a solid, Perry’s method for finding, 96—98 
bollard friction, use of, in drawing wire, 39 

D. 


S 


258 


INDEX 


Friction— continued. 

comparison between fluid and solid, 19 

Cotterill’s graphic method of showing value of friction of a band 
on a cylinder, 26—28 

diagram on squared paper of values, 23—25 
experimental determination and table of results, 19—20 
experiments on friction of a band on a pulley or wheel, 31—38 
graphical method for showing value of, 25—26 
lateral friction, 41—43 
laws of, 17—19 

logarithmic and semi-logarithmic paper for representing laws of 
26—28 

logarithmic spiral, mechanical method of drawing, 30—32 
mechanical relay, 39—41 

method of least squares applied to calculation of coefficient of, 
21—23 

of water, method of finding, 95—98 
Friction brakes, 67—94 
Froude, E. R., F.R.S., 

assistance to author acknowledged, 16 
note on oscillations in block brake dynamometers, 88 
ship model testing at Haslar, 4, 236, 238 
Froude, William, F.R.S., 

diagrammatic registration of power in ship testing, 47 
experiments on causes of resistance of ships and propositions on 
stream lines, 3—4, 139—142, 236 

reproduction of diagrams and matter from a paper by, per¬ 
mission acknowledged, 16 
researches on laws of friction, 18, 83—84 
ship model tests, 2, 236—238 

statement on importance of dynamometric tests of ships’ engines. 
107 

transmission dynamometer, 162—168 
turbine dynamometer, and his paper on it, 2, 78, 98—108 
Froude water brake dynamometer, of Heenan and Froude, 108—111 

Galvanometers, construction of the magnetic needle type, 122 

Garret, R., & Sons, water-cooled brake dynamometer, 90 

Gewerbschaft Wilkowitz, torsion test of propeller shaft, 208 

Gravity dynamometers, method explained, 5—15 

Gray, Dr. J. G., use of mechanical relay, 40 

Greenhill, Prof. A. G., article on theory of the planimeter, 50 

Gregory, Olinthus, mention of horse-power in 1805...9 

Greyhound, H.M.S., Froude’s experiments on, 237 

Griffin Engineering Co., Ltd., absorption dynamometer, 91—93 

Griffin gas engine, trial by Society of Arts, 76 

Haslar, Admiralty tank and equipment for ship model testing, 4, 
236, 238—244, 245, 246 


INDEX 


259 


Ilastig, investigations of, respecting lathe tool dynamometer, 93 
Heat, Joule’s determination of mechanical equivalent, 14—15 
Heenan and Froude, Froude water brake dvnamometer of, 105, 108— 

111 

Hefner Alteneck, F. von, transmission dynamometer of. 174 
Hele-Shaw, Professor H. S., 

experiments on stream lines, 135, 136—139 
paper on mechanical integrators, 50 
Henrici, Prof. 0., F.P.S., explanation of the Amsler polar plani- 
meter, 54 

Herschel, Sir John, electrical experiments, 121 
Hirn, Gr. A., 

apparatus for finding heat produced by friction of water, 95—96 
band machine, 13 

method of studying air resistance, 247 
researches on laws of friction, 18 
torsion meter, 2, 195—196 

Iioldsworth, H., invention of differential gear, 196 
Hopkinson, Prof. B., F.R.S., 

assistance to author acknowledged, 16 
torsion meter, 212—215 

Hopkinson, Prof. John, F.R.S., use of rope brake in trials of 
engines, 76 

Hopps, James, of Cooper’s Hill College, additions to friction brake 
devised by, 80 

Horizontal impulse wheel, Borda’s experiments by means of gravity 
method, 7 
Horse-power, 

estimates of force by, methods employed, 8—9 
first mention in print, 9 

Hutton, James, method of studying problem of air resistance in 
1787...247 

Hydraulic dynamometers. See Water Brakes. 

Imray, J., 

brake dynamometer, 82—85 

experiments for finding coefficients of friction, 32—33, 34—37 
Institution of Naval Architects, ship model testing tank at Teddington 
initiated by, 245 

Integrators, applied to work 'measuring machines, 45—50, 58—66, 151— 
155 

Internal combustion engines, 

dynamometric tests, 223—235 

suitability of the Griffin Engineering Co.’s brake for testing 
petrol motors, 92 

Watson’s diaphragm for finding horse-power, 224 

“ J ack-in-the-box/’ mechanism known as, 196 
Japan, ship model testing tank, 246 


“s' 2 


260 


INDEX 


Jervis-Smith, F. J., 

cradle dynamometer, 218—220 

electrical method of reading the torsional angle, 202—203 
end thrust brakes, 125—127 
“ Rotostat,” 198—201 
torsion meter, 196—202 
transmission dynamometer, 168—171 
Johnson, Charles, experiments on electrical method of reading the 
torsional angle, 205—206, 212 
Johnson, C. H., torsion meter, 217 
Joule, James Prescott, F.R.S., 

gravity method of measuring work, 14—15 
water friction experiments, 96 

Kaiser Wilhelm II., S.S., reading of torsional angle on, 210—211 
Kapp, Gisbert, remarks on the Saurin marine dynamometer, 180 
Kelvin, William Thomson, Lord, rope dynamometer brake of, 2, 72—75 
Kelvin and James White Works, 217 

Kennedy, Prof. Alexander, F.R.S., use of rope brake in trial of 
engines, 76 

King, C. R., on draw-bar dynamometers, 189 
King dynamometer, 175 
King Edward, H.M.S., 190 
Knife-edge suspension, 

machines of Marcel Deprez, 222 
method employed by Dr. Drysdale, 220—221, 225 
observations on, 220—221 
Krupp, F., torsion test of propeller shaft, 208 

Lanchester, F. W., 
accelerometer, 229 

worm drive dynamometer, 184—189 
Langley, method of studying air resistance, 247 
Latchinoff, M., dynamometer, 178 
Lateral friction, 41—43 

Least squares, method of, application to calculation of coefficient 
of friction, 21—23 

Logarithmic ruling, for representation of laws of friction, 26—28 
Logarithmic spiral, mechanical method of drawing, 30—32 
Longmans, Green & Co., assistance to author acknowledged, 16 
Luckhardt and Alten, Cassel, pamphlet on planimeters, 50 
Ludot, re-invention of method of winding up weights by ropes, 71 
Lux, Fritz, torsion meter, 217 

Mallock, A., paper on experiments in engineering workshop at Cam¬ 
bridge, 1881...93 
Man’s labour, 

Coulomb’s method for utilising, 10—12, 128—131 
Prony’s note on Coulomb’s method, 131—133 


INDEX 


261 


Marey, M., air movements studied by means of chromophotography, 

135—136 

Matter, M., dynamometer, 174—175 

Mean line of force for dynamometric diagrams, method of finding, 66 

Mechanical relay, 39—41 

Megy, M., dynamometer, 176—177 

Method of least squares. See Least Squares,, Method of. 

Michigan, ship model testing tank, 246 
Millard Engineering Laboratory, Oxford, 

experiments on dynamometric measurements, 3 
method of testing prime-movers at, 225 
torsional form of ergometer used, 61 
Milling machine supports, use in dynamometric tests, 225—226 
Model shaping machine at Haslar, described, 240—244 
Model ship testing. See Ship Model Testing. 

Moore, A. E., cradle dynamometer, 222 

Moore, C. R., direct reading electrical dynamometer, 182—184 
Morgan, Prof. W., investigation on the air brake, 115 
Morin, General A., 

description of his dynamometric machines and instruments, 2, 
145—161 

recording apparatus (1841), 45—46 
Morris and Lister, eddy current testing brake, 122—124 
Motor car engines, testing by the Wimperis accelerometer, 229—235 

National Physical Laboratory, 
aeronautic dynamometer, 247 
testing tank for ship models, 244—245 
Neer, dynamometer of, 177—178 

Nicholson, Prof. J. T., lathe tool dynamometer, 93—94 

Paper band registering apparatus, 46 

Paris, Dr., thaumatrope of, 201 

Paris, ship model testing tank at, 246 

Parsons, Hon. R. C., dynamometer, 179 

Paxman portable steam engine, trial by Society of Arts, 76 

Penn, John, recognition of importance of dynamometers, 3 

Perry, Prof. John, F.R.S., 

comparison between solid and fluid friction, 18, 19 
experiment on measuring force, 7 

method for finding friction between a liquid and a solid, 96 98 
Peter Brotherhood fluid friction dynamometer, 111—112 
Planimeters, 

description and explanation of, 51—57, 64—66 
Ernst’s integrator for finding quadrature of the curve, 151—155 
example of use in dynamometry, 64—66 
Polar planimeter. See Amsler Polar Planimeter. 

Poncelet, J. V., on Coulomb’s discoveries for utilising men’s labour, 
10—11 

Power diagram of the Matter dynamometer, 174 175 


262 


INDEX 


Probability, theory of, 21 
Prony, 

friction dynamometer, 2, 86—88 
note on memoir of Coulomb, 131—133 
Propeller shafts, 

calibration of, recommendations for, 214—215 
investigation of torsional stresses, 206—208 

Quadrature of the curve, observations on and methods of finding, 
150—155 

Queen Alexandra, S.S., electrical method of reading torsional angle 
applied to, 203, 204 

Baffard, I., Carpentier’s dynamometer remodelled and improved by, 
85 

Rankine, W. J. M., F.R.S., application of Simpson method of finding 
areas, 53 

Ransomes, Sims and Jefferies, use of Balk’s brake dynamometer, 90 
Rayleigh, Lord, 

optical arrangement for viewing mixed colours, 199 

method for reading speed of shaft referred to, 172 
Reaction, dynamometric, principle of Froude’s turbine dynamometer 
explained, 103—104, 105 
Reckenzaun, A., brake dynamometer, 85 
Recording apparatus, 

method employed on Froude’s turbine dynamometer, 106 
used in conjunction with dynamometers, 45—66, 106 
Renard, Col., experiments with an air brake, 114—115 
Reynolds, Prof. Osborne, 

investigations on critical velocity, 98, 142—143 
researches on laws pf friction, 18 
Avater brake used by, in 1876...98 
Robins, method of studying air resistance in 1746...247 
Roget, Dr., log log slide rule invented by, 32 
Rope brakes, 

application of, 76—82 
Carpentier’s dynamometer, 85—86 
early application of coiled rope, 67—68 
modification of Thomson brake, 77—78 
resistance of coiled rope on a cylinder, 68—69 
rope dynamometer brake, 71—75 

Rotation, speed of, principle of Froude’s turbine dynamometer ex¬ 
plained, 102—104 

Rotational dynamometer of Morin, 158—161 
Rotostat, instrument, 197—201 
Royal Agricultural Society, 

Appold and Amos friction brake as used by, 89 
dynamometric measurements by, 4 
Ruddick, dynamometer of, 177 


INDEX 


263 


Sankey, Captain Riall, 
engine testing, 4 

figure of rope brake reproduced from paper in Engineering Maga¬ 
zine , 77—78 

Saurin, M., marine- dynamometer, 180 

Sautter Lemonner, of Paris, makers of the Megy dynamometer, 176 
Scheibe, brake dynamometer of, 86 
Shafts, propeller. See Propeller Shafts. 

Shaw, F., cradle dynamometer employed by, 222 
Shaw, Prof. Hele. See Hele Shaw, Prof. 

Ship model testing, 

apparatus described, 238—245 
diagrammatic method of registering power, 47 
example of dynamometer record^ 64—66 
experimental tanks, list of and details given, 245—246 
Froude’s original researches, 236—238 
methods employed, 1—2, 4, 168, 237 
Ships, 

causes of resistance of, Froude’s lecture on, 139—142 
importance of dynamometric tests of engines, 107 
machines for testing. See Dynamometers, and Ship Model Test¬ 
ing, above. 

unloading of, method employed, 11—12 
Siemens, 

coupling of, 224 
differential governor of, 196 
Simpson, method of finding areas, 53 
Skin friction, cause of resistance of ships, 140—141 
Slide rules, employed by Watt, 9 
Smeaton, John, F.R.S. V 

method of measuring work, 5—7 
method of studying air resistance (1759)...247 
Smith, Prof. R. H., experiments respecting lathe tool dynamometer, 
93—94 

Society of Arts, 

dynamometric tests for electric lighting, 4 
rope brake used in trial of machines, 76—77 
Soho sliding rule, 9 
Southern, engineer, 

invention of steam engine indicator, 44 
slide rules devised by, 9 
Speed, 

Frahm speed-indicator described, 206 
instability of, with friction brakes, 226—227 
optical methods of reading, 172—173 
Spezia, ship model testing tank, 245 

Spon, E. and F. N., pamphlet on work measuring machines, quoted, 
125—126, 171 


264 


INDEX 


Springs, 

arrangement for obtaining a permanent trace of the deflections, 
149 

arrangement of the blades, 147—149 
curved, used on Saurin’s marine dynamometer, 180 
longitudinal profile of, 147 
method of moving traced paper, 149—150 
relationship between the different proportions of, 147 
rules for finding the proportions of, 146—147 
Steam engine indicator, 

Ashton and Storey’s, 46 
invention by Southern, 44—45 
Steam engines, 

estimation of force by horse-power, 8—9 

power measuring machines. See Dynamometers. 

Stokes, Sir George, on stream lines, 136—137 
Stream line motion, 

absence of resistance to an immersed body, Froude’s lecture, 140, 
141—142 

experiments on and colour used to render motion visible, 135—139 


Tatham, dynamometers of, 178—179 
Taurines, M. See Saurin. 

Taylor and Francis, Messrs., assistance to author acknowledged, 16 
Temperature, air brake experiments, 116—117 

Tension, method of utilising ill equality of, in belt dynamometers, 162— 
165 

Thaumatrope of Dr. Paris, 201 
Thompson, Prof. S. P., F.E.S., 

article on dynamo electric machinery, 168 
assistance to author acknowledged, 16 
description of Jervis-Smith’s cradle dynamometer, 218 
Thomson, Prof. James, brake dynamometer, 82 
Thomson, William. See Kelvin, Lord. 

Thring, L. G. P., torsion meter, 212—215 
Thurston, A. P., torsion meter, 217 
Thurston, Mr., U.S.A., 

block brake dynamometer, 87 
researches on laws of friction, 18 
Toggle lever, objection to use in dynamometers, 89 
Tools, cutting of, Nicholson’s lathe tool dynamometer, 93—94 
Torquay, ship model testing tank, 236, 245 
Torque, 

principle of the Lanchester worm drive dynamometer explained, 
185—188 

word invented by Prof. James Thomson, 82 
Torsion, angle of, 

electrical methods of reading, 202—206 


INDEX 


265 


Torsion, angle of— continued. 

mechanical method of reading, 196—197 
method of calculating by torsion meters, 191—191 
optical methods of reading, 197—202 
Torsion meters, 

Amsler, 215—216 
Broughton, 216—217 
Denny-Johnson, 212 
Fottinger, 209—212 
Frahm, 206—208 
Hirn, 195—196 

Hopkinson and Thring, 212—215 
Jervis-Smith, 196—202 
Johnson, C. H., 217 
Lux, 217 
Necessity for, 190 

principle underlying construction of, 190—191 
Thurston, 217 

Torsional stresses on propeller shafts, investigation of, 206—208 
Tower, Beauchamp, 

researches on laws of friction, 18 
use of rope brake in trial of engines, 76 
Transmission dynamometers, 

Amsler, 181—182 
Ayrton and Perry, 173 
Bourry, 176 
Boys, C. V., 175—176 
Dalby, 180—181 

Easton and Anderson’s, 161—162 
Farcot, 179 

Froude, William, 162—168 
function of, 144—145 
Hefner Alteneck, F. von, 174 
Jervis-Smith, 168—171 
King, 175 

Lanchester’s worm drive dynamometer, 184—189 
Latchinoff, 178 
. Matter, 174—175 
Megy, 176—177 

Moore’s direct reading electrical dynamometer, 182—184 
Morin’s description of his machines and instruments, 145—161 
Neer, 177—178 
Parsons, 179 
Rudclick, 177 

Saurin’s marine dynamometer, 180 
Tatham, 178—179 
Yalet, 177 

Transverse elasticity, term Gr the coefficient of, 192 
Tudsbery, J. H. T., assistance to author acknowledged, 15, 16 

D. * T 


266 


INDEX 


Turbine dynamometer of Froude, description and explanation, 98— 
108 

Uebigau, ship model testing tank, 245, 246 
Ulysses, use of coiled rope, 67—68 
Unit of work, inch-ounce of Smeaton, 7 
Unwin, Prof. W. C., F.R.S., 

drawing of brake of experimental engine at Central .Technical 
College, 78—79 
flexible band brake, 75—76 
on the coefficient of transverse elasticity, 192 

Valet, M., dynamometer, 177 
Vehicles, 

differential gear invented by Holdsworth, 196 
method of measuring work done by, 9—10 
Morin’s dynamometer for measuring work of, 155—158 
Vicker, Sons and Maxim’s works, air propeller testing plant at, ^49— 
252 

Vincennes, fort of, method employed of utilising men’s labour, 11 
Violle, experiment for estimating heating effect of eddy current, 122 
Vortex motion, principle of Froude’s turbine dynamometer explained, 
103—104 

Walkek, W. G., & Co., 

assistance to author acknowledged, 16 
invention of air brake, 113—114 
Ward, Mr., paper upon road wheels and roads, 1809... 10 
Washington, ship model testing tank, 245, 246 
Water, 

critical velocity investigation, 142—143 
friction of, methods of finding, 95—98 
Water brakes, 

Froude’s turbine dynamometer, 98—108 

Froude water brake djmamometer, of Heenan and Froude, 108— 
111 

historical account, 95—98 

Peter Brotherhood fluid friction dynamometer, 111—112 
Water-cooled brake dynamometers, 90—93 
Watson, Prof. W., F.R.S., 

cradle dynamometer, 227—228 
diaphragm, 224 
on the petrol engine, 224 
Watt, James, 

construction of force-measuring apparatus, 146 
method of determining horse-power, 8—9 
Watt-Southern steam engine indicator, invention of, 44—45 
Wave-making, cause of resistance of ships, 140—141 


INDEX 


267 


White, Sir William, 

“ Manual of Naval Architecture,” 236, 238 
on model ship testing apparatus, 239 
White and Poppe air brake, description and formula, 117—118 
Willans and Robinson’s engineering works, Rugby, engine testing 
at, 4, 77 

Willis, R., F.R.S., reproduction from, of Wren’s invention for winding 
up weights, 70 

Wimperis accelerometer, construction described, 229—235 
Winchester College, physical laboratory of, 31 
Windmill, Jervis-Smith’s ergometer applied to, 125 
Windmill test, Smeaton’s use of, for measuring work, 5—7 
Wingfield, C. H., 

engine testing, 4 

figure of rope brake reproduced, 77—78 
Wire drawing, use of bollard friction in, 39 

Witz, Prof. Aime, account of Col. Renard’s experiments with an air 
brake, 114 

Wood, E. B., investigation on the air brake^ 115 

Worm drive, measure of efficiency by the Lanchester dynamometer, 
184—189 

Worm drive dynamometer of Lanchester, 184—189 
Wren, Sir Christopher, invention for winding up weights by ropes, 
69—71 

Yarrow, A. F., donation for construction of testing tank for ship 
models, 245 

Zodel-Yoith coupling, 222, 227 


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Bruce, E. M. Pure Food Tests.i2mo, *1 25 

Bruhns, Dr. New Manual of Logarithms.8vo, cloth, 2 00 

half morocco, 2 50 

Brunner, R. Manufacture of Lubricants, Shoe Polishes and Leather 

Dressings. Trans, by C. Salter.8vo, *3 00 

Buel, R. H. Safety Valves. (Science Series No. 21.).i6mo, o 50 

Burns, D. Safety in Coal Mines.i2mo, *1 00 

Burstall, F. W. Energy Diagram for Gas. With Text.8vo, 1 50 

-Diagram. Sold separately. *1 00 

Burt, W. A. Key to the Solar Compass.i6mo, leather, 250 

Burton, F. G. Engineering Estimates and Cost Accounts.i2mo, *1 50 

Buskett, E. W. Fire Assaying.i2mo, *1 25 

B utler, H. J. Motor Bodies and Chassis.8vo, *2 50 

Byers, H. G., and Knight, H. G. Notes on Qualitative Analysis ... .8vo, *1 50 

Cain, W. Brief Course in the Calculus.i2mo, *1 75 

-Elastic Arches. (Science Series No. 48.).i6mo, o 50 

-Maximum Stresses. (Science Series No. 38.).i6mo, o 5G 

-Practical Designing Retaining of. Walls. (Science Series No. 3.) 

i6mo, o 50 

-Theory of Steel-concrete Arches and of Vaulted Structures. 

(Science Series No. 42.).i6mo, o 50 

-Theory of Voussoir Arches. (Science Series No. 12.).i6mo, o 50 

-Symbolic Algebra. (Science Series No. 73.).i6mo, o 50 

Campin, F. The Construction of Iron Roofs.8vo, 2 00 

Carpenter, F. D. Geographical Surveying. (Science Series No. 37.).i5mo, 
Carpenter, R. C., and Diederichs, H. Internal Combustion Engines.. 8vo, *5 00 
Carter, E. T. Motive Power and Gearing for Electrical Machinery. 8vo, *5 00 

Carter, H. A. Ramie (Rhea), China Grass.i2mo, *2 00 

Carter, H. R. Modern Flax, Hemp, and Jute Spinning.8vo, *3 00 

Cary, E. R. Solution of Railroad Problems with the Slide Rule i6mo, *1 00 

Cathcart, W. L. Machine Design. Part I. Fastenings.8vo, *3 00 

Cathcart, W. L., and Chaffee, J. I. Elements of Graphic Statics. . .8vo, *3 00 

-Short Course in Graphics.i2mo, 1 50 

Caven, R. M., and Lander, G. D. Systematic Inorganic Chemistry.i2mo, *2 00 

Chalkley, A. P. Diesel Engines.8vo, *3 00 

Chambers’ Mathematical Tables.8vo, 1 75 

Chambers, G. F. Astronomy. i6mo, *1 50 

Charpentier, P. Timber..... ... 8vo, *6 00 



































D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 


7 


Chatley, H. Principles and Designs of Aeroplanes. (Science Series 

No. 126).i6mo, o 50 

-How to Use Water Power.i2mo, *1 00 

-Gyro static Balancing.8vo, *1 00 

Child, C. D. Electric Arc.8vo, *2 00 

Child, C. T. The How and Why of Electricity.i2mo, 1 00 

Christian, M. Disinfection and Disinfectants. Trans, by Chas. 

Salter.i2mo, 2 00 

Christie, W. W. Boiler-waters, Scale, Corrosion, Foaming.8vo, *3 00 

-Chimney Design and Theory.8vo, *3 00 

-Furnace Draft. (Science Series No. 123.).i6mo, o 50 

-Water: Its Purification and Use in the Industries.8vo, *2 00 

Church’s Laboratory Guide. Rewritten by Edward Kinch.8vo, *250 

Clapperton, G. Practical Papermaking.8vo, 2 50 

Clark, A. G. Motor Car Engineering. 

Vol. I. Construction. *3 00 

Vol. II. Design.( In Press.) 

Clark, C. H. Marine Gas Engines.i2mo, *1 50 

Clark, D. K. Fuel: Its Combustion and Economy.i2mo, 1 50 

Clark, J. M. New System of Laying Out Railway Turnouts.i2mo, 1 00 

Clarke, J. W., and Scott, W. Plumbing Practice. 

Vol. I. Lead Working and Plumbers’ Materials.8vo, *4 00 

Vol. II. Sanitary Plumbing and Fittings. (In Press.) 

Vol. III. Practical Lead Working on Roofs. (In Press.) 

Clausen-Thue, W. ABC Telegraphic Code. Fourth Edition . . . i2mo, *5 00 

Fifth Edition. . . ..8vo, *7 00 

-- The A 1 Telegraphic Code.8vo, *7 50 

Clerk, D., and Idell, F. E. Theory of the Gas Engine. (Science Series 

No. 62.).i6mo, 050 

Clevenger, S. R. Treatise on the Method of Government Surveying. 

i6mo, morocco, 2 50 

Clouth, F. Rubber, Gutta-Percha, and Balata.8vo, *5 00 

Cochran, J. Concrete and Reinforced Concrete Specifications.8vo, *2 50 

-Treatise on Cement Specifications.8vo, *1 00 

Coffin, J. H. C. Navigation and Nautical Astronomy.i2mo, *3 50 

Colburn, Z., and Thurston, R. H. Steam Boiler Explosions. (Science 

Series No. 2.).i6mo, o 50 

Cole, R. S. Treatise on Photographic Optics.i2mo, 1 50 

Coles-Finch, W. Water, Its Origin and Use.8vo, *5 00 

Collins, J. E. Useful Alloys and Memoranda for Goldsmiths, Jewelers. 

i6mo, o 50 

Collis, A. G. High and Low Tension Swit:h-Gear Design.8vo, *3 50 

-Switchgear. (Installation Manuals Series.).izmo, *050 

Constantine, E. Marine Engineers, Their Qualifications and Duties. 8vo, *2 00 

Coombs, H. A. Gear Teeth. (Science Series No. 120.).i6mo, 050 

Cooper, W. R. Primary Batteries.8vo, *4 00 

-“ The Electrician ” Primers. 8vo, *5 00 

Part I. * I 50 

Part II. * 2 50 

Part III. *200 









































8 D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 

Copperthwaite, W. C. Tunnel Shields.4to, *9 00 

Corey, H. T. Water Supply Engineering.8vo (In Press.) 

Corfield, W. H. Dwelling Houses. (Science Series No. 50.).... i6mo, o 50 

-Water and Water-Supply. (Science Series No. 17.).i6mo, o 50 

Cornwall, H. B. Manual of Blow-pipe Analysis.8vo, *2 50 

Courtney, C. F. Masonry Dams.8vo, 350 

Cowell, W. B. Pure Air, Ozone, and Water.i2mo, *2 00 

Craig, T. Motion of a Solid in a Fuel. (Science Series No. 49.). i6mo, o 50 

-Wave and Vortex Motion. (Science Series No. 43.).i6mo, o 50 

Cramp, W. Continuous Current Machine Design.8vo, *250 

Creedy, F. Single Phase Commutator Motors.8vo, *2 00 

Crocker, F. B. Electric Lighting. Two Volumes. 8vo. 

Vol. I. The Generating Plant. 3 0 ) 

Vol. II. Distributing Systems and Lamps. 

Crocker, F. B., and Arendt, M. Electric Motors.8vo, *2 50 

Crocker, F. B., and Wheeler, S. S. The Management of Electrical Ma¬ 
chinery.i2mo, *1 00 

Cross, C. F., Bevan, E. J., and Sindall, R. W. Wood Pulp and Its Applica¬ 
tions. (Westminster Series.).8vo, *2 00 

Crosskey, L. R. Elementary Perspective.8vo, 1 00 

Crosskey, L. R., and Thaw, J. Advanced Perspective.8vo, 1 50 

Culley, J. L. Theory of Arches. (Science Series No. 87.).i6mo, 050 

Dadourian, H. M. Analytical Mechanics.i2mo, *3 00 

Danby, A. Natural Rock Asphalts and Bitumens.8vo, *250 

Davenport, C. The Book. (Westminster Series.).8vo, *2 00 

Davey, N. The Gas Turbine.8vo, *4 00 

Davies, D. C. Metalliferous Minerals and Mining.8vo, 5 00 

-- Earthy Minerals and Mining...8vo, 5 00 

Davies, E. H. Machinery for Metalliferous Mines.8vo, 8 00 

Davies, F. H. Electric Power and Traction.8vo, *2 00 

-Foundations and Machinery Fixing. (Installation Manual Series.) 

i6mo, *1 00 

Dawson, P. Electric Traction on Railways.8vo, *9 00 

Day, C. The Indicator and Its Diagrams.i2mo, *2 00 

Deerr, N. Sugar and the Sugar Cane.8vo, *8 00 

Deite, C. Manual of Soapmaking. Trans, by S. T. King.4to, *500 

De la Coux, H. The Industrial Uses of Water. Trans, by A. Morris. 8vo, *4 50 

Del Mar, W. A. Electric Power Conductors.8vo, *2 00 

Denny, G. A. Deep-level Mines of the Rand.4to, *1000 

-Diamond Drilling for Gold. *5 00 

De Roos, J. D. C. Linkages. (Science Series No. 47.).i6mo, o 50 

Derr, W. L. Block Signal Operation.Oblong i2mo, *1 50 

-Maintenance-of-Way Engineering. (In Preparation.) 

Desaint, A. Three Hundred Shades and How to Mix Them.8vo, *10 00 

De Varona, A. Sewer Gases. (Science Series No. 55.).i6mo, o 50 

Devey, R. G. Mill and Factory Wiring. (Installation Manuals Series.) 

i2mo, *1 00 

Dibdin, W. J. Public Lighting by Gas and Electricity.8vo, *8 00 

—— Purification of Sewage and Water.8vo, 6 50 









































D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 


9 


L ichmann, Carl. Basic Open-Hearth Steel Process.i2mo, *3 50 

Dieterich, K. Analysis of Resins, Balsams, and Gum Resins.8vo, *3 00 

Dinger, Lieut. H. C. Care and Operation of Naval Machinery. . . i2mo, *2 00 


Dixon, D. B. Machinist’s and Steam Engineer’s Practical Calculator. 

i6mo, morocco, j 25 

Doble, W. A. Power Plant Construction on the Pacific Coast (In Press.) 


Dommett, W. E. Motor Car Mechanism.i2mo, *1 25 

Dorr, B. F. The Surveyor’s Guide and Pocket Table-book. 

i6mo, morocco, 2 00 

Down, P. B. Handy Copper Wire Table.i6mo, *1 00 

Draper, C. H. Elementary Text-book of Light, Heat and Sound . . i2mo, 1 00 

-Heat and the Principles of Thermo-dynamics.i2mo, *200 

Dubbel, H. High Power Gas Engines._.8vo, *5 00 

Duckwall, E. W. Canning and Preserving of Food Products.8vo, *5 00 

Dumesny, P., and Noyer, J. Wood Products, Distillates, and Extracts. 

8vo, *4 50 


Duncan, W. G., and Penman, D. The Electrical Equipment of Collieries. 

8vo, *4 00 

Dunstan, A. E., and Thole, F. B. T. Textbook of Practical Chemistry. 

i2mo, *1 40 

Duthie, A. L. Decorative Glass Processes. (Westminster Series.) .8vo, *200 


Dwight, H. B. Transmission Line Formulas.8vo, *2 00 

Dyson, S. S. Practical Testing of Raw Materials.8vo, *5 00 

Dyson, S. S., and Clarkson, S. S. Chemical Works.8vo, *7 50 

Eccles, R. G., and Duckwall, E. W. Food Preservatives .... 8vo, paper, o 50 

Eck, J. Light, Radiation and Illumination. Trans, by Paul Hogner, 

8vo, *2 50 

Eddy, H. T. Maximum Stresses under Concentrated Loads.8vo, 1 50 

Edelman, P. Inventions and Patents.i2mo. (In Press.) 

Edgcumbe, K. Industrial Electrical Measuring Instruments.8vo, *250 

Edler, R. Switches and Switchgear. Trans, by Ph. Laubach. . .8vo, *4 00 

Eissler, M. The Metallurgy of Gold.8vo, 7 50 

-The Hydrometallurgy of Copper.8vo, *4 50 

-The Metallurgy of Silver.8vo, 4 00 

-The Metallurgy of Argentiferous Lead.8vo, 5 00 

-A Handbook on Modern Explosives.8vo, 5 00 

Ekin, T. C. Water Pipe and Sewage Discharge Diagrams.folio, *3 00 

Eliot, C. W., and Storer, F. H. Compendious Manual of Qualitative 

Chemical Analysis.i2mo, *1 25 

Ellis, C. Hydrogenation of Oils.8vo, *4 00 

Ellis, G. Modern Technical Drawing.8vo, *2 00 

Ennis, Wm. D. Linseed Oil and Other Seed Oils.8vo, *4 00 

-Applied Thermodynamics.8vo, *4 50 

-Flying Machines To-day.i2mo, *4 50 

-Vapors for Heat Engines.i2mo, *1 00 

Erfurt, J. Dyeing of Paper Pulp. Trans, by J. Hubner.8vo, *7 50 

Ermen, W. F. A. Materials Used in Sizing.8vo, *2 00 

Evans, C. A. Macadamized Roads. (In Press.) 
































io D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 


Ewing, A. J. Magnetic Induction in Iron.8vo, *4 oc 

Fairie, J. Notes on Lead Ores.12010, *1 00 

-Notes on Pottery Clays.i2mo, *1 50 

Fairley, W., and Andre, Geo. J. Ventilation of Coal Mines. (Science 

Series No. 58.).i6mo, o 50 

Fair weather, W. C. Foreign and Colonial Patent Laws.8vo, *3 00 

Fanning, J. T. Hydraulic and Water-supply Engineering.8vo, *5 00 

Fauth, P. The Moon in Modern Astronomy. Trans, by J. McCabe. 

8vo, *2 00 

Fay, I. W. The Coal-tar Colors.8vo, *4 00 

Fernbach, R. L. Glue and Gelatine.8vo, *3 00 

-Chemical Aspects of Silk Manufacture.nmo, *1 00 

Fischer, E. The Preparation of Organic Compounds. Trans, by R. V. 

Stanford. nmo, *1 25 

Fish, J. C. L. Lettering of Working Drawings.Oblong 8vo, 1 00 

Fisher, H. K. C., and Darby, W. C. Submarine Cable Testing . . . .8vo, *3 50 

Fleischmann, W. The Book of the Dairy. Trans, by C. M. Aikman. 

8vo, 4 00 


Fleming, J. A. The Alternate-current Transformer. Two Volumes. 8vo. 

Vol. I. The Induction of Electric Currents. 

Vol. II. The Utilization of Induced Currents. 

Fleming, J. A. Propagation of Electric Currents.8vo, 

-- Centenary of the Electrical Current.8vo, 

-Electric Lamps and Electric Lighting.8vo, 

-Electrical Laboratory Notes and Forms.4to, * 

-A Handbook for the Electrical Laboratory and Testing Room. Two 

Volumes.8vo, each, * 

Fleury, P. Preparation and Uses of White Zinc Paints.8vo, 

Fleury, H. The Calculus Without Limits or Infinitesimals. Trans, by 

C. O. Mailloux. (In Press.) 

Flynn, P. J. Flow of Water. (Science Series No. 84.).i2mo, 

-- Hydraulic Tables. (Science Series No. 66.).i6mo, 

Foley, N. British and American Customary and Metric Measures. . folio, 
Forgie, J. Shield Tunneling.8vo. (In Press.) 

Foster, H. A. Electrical Engineers’ Pocket-book. (Seventh Edition.) 

i2mo, leather, 

-Engineering Valuation of Public Utilities and Factories.8vo, 

-Handbook of Electrical Cost Data.8vo (In Press.) 

Foster, Gen. J. G. Submarine Blasting in Boston (Mass.) Harbor 4to, 

Fowle, F. F. Overhead Transmission Line Crossings.nmo, 

-The Solution of Alternating Current Problems.8vo (In Press.) 

Fox, W. G. Transition Curves. (Science Series No. no.).i6mo, 

Fox, W., and Thomas, C. W. Practical Course in Mechanical Draw¬ 
ing.nmo, 

Foye, J. C. Chemical Problems. (Science Series No. 6p.).i6mo, 

-Handbook of Mineralogy. (Science Series No. 86.).i6mo, 

Francis, J. B. Lowell Hydraulic Experiments.4to, 

Franzen, H. Exercises in Gas Analysis.. ...nmo, 


00 

00 

00 

50 

00 

00 


5 00 
2 50 


o 50 
o 50 
3 00 


5 00 
‘3 00 

3 53 
'i 5» 

o 50 


1 25 
o 50 
O 50 
15 00 
*1 00 







































D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 


II 

Freudemacher, P. W. Electrical Mining Installations. (Installation 

Manuals Series.). . * x 00 

Frith, J. Alternating Current Design.8vo, *2 00 

Fritsch, J. Manufacture of Chemical Manures. Trans, by D. Grant. 

8vo, *4 00 

Frye, A. I. Civil Engineers’ Pocket-book.i2mo, leather, *5 00 

Fuller, G. W. Investigations into the Purification of the Ohio River. 

4to, *10 00 

Furnell, J. Paints, Colors, Oils, and Varnishes.8vo. *1 00 

Gairdner, J. W. I. Earthwork.8vo ( In Press.) 

Gant, L. W. Elements of Electric Traction.8vo, *2 50 

Garcia, A. J. R. V. Spanish-English Railway Terms.8vo, *450 

Garforth, W. E. Rules for Recovering Coal Mines after Explosions and 

Fires...i2mo, leather, 1 50 

Gaudard, J. Foundations. (Science Series No. 34.).i6mo, 050 

Gear, H. B., and Williams, P. F. Electric Central Station Distribution 

Systems.8vo, *3 00 

Geerligs, H. C. P. Cane Sugar and Its Manufacture.8vo, *5 00 

-World’s Cane Sugar Industry.8vo, *5 00 

Geikie, J. Structural and Field Geology. 8vo, *4 00 

-Mountains. Their Growth, Origin and Decay.8vo, *400 

-The Antiquity of Man in Europe.8vo, *3 00 

Georgi, F., and Schubert, A. Sheet Metal Working. Trans, by C. 

Salter.8vo, 3 00' 

Gerber, N. Analysis of Milk, Condensed Milk, and Infants’Milk-Food. 8vo, 1 25 
Gerhard, W. P. Sanitation, Watersupply and Sewage Disposal of Country 

Houses.i2mo, *2 00 

-Gas Lighting (Science Series No. hi.) .i6mo, o 50 

-Household Wastes. (Science Series No. 97.).i6mo, o 50 

-House Drainage. (Science Series No. 63.).i6mo, o 50 

Gerhard, W. P. Sanitary Drainage of Buildings. (Science Series No. 93.) 

i6mo, 0 50 

Gerhardi, C. W. H. Electricity Meters.8vo, *4 00 

Geschwind, L. Manufacture of Alum and Sulphates. Trans, by C. 

Salter.8vo, *5 00 

Gibbs, W. E. Lighting by Acetylene.i2mo, *1 50 

-Physics of Solids and Fluids. (Carnegie Technical School’s Text¬ 
books.). *1 50 

Gibson, A. H. Hydraulics and Its Application.8vo, *5 00 

-Water Hammer in Hydraulic Pipe Lines.i2mo, *2 00 

Gilbreth, F. B. Motion Study.i2mo, *2 00 

-Primer of Scientific Management.i2mo, *1 00 

Gillmore, Gen. Q. A. Limes, Hydraulic Cements ard Mortars.8vo, 400 

-Roads, Streets, and Pavements.i2mo, 2 00 

Golding, H. A. The Theta-Phi Diagram.i2mo, *1 25 

Goldschmidt, R. Alternating Current Commutator Motor.8vo, *300 

Goodchild, W. Precious Stones. (Westminster Series.).8vo, *200 

Goodeve, T. M. Textbook on the Steam-engine.nmo, 2 00 

Gore, G. Electrolytic Separation of Metals. 8vo, *3 50 




































12 


D. VAN NOSTRAND CO/S SHORT TITLE CATALOG 


Gould, E. S. Arithmetic of the Steam-engine.i2mo, i oo 

-Calculus. (Science Series No. 112.).i6mo, 050 

-High Masonry Dams. (Science Series No. 22.).i6mo, o 50 

-Practical Hydrostatics and Hydrostatic Formulas. (Science Series 

No. 117.).i6mo, 050 

Gratacap, L. P. A Popular Guide to Minerals.8vo, *3 00 

Gray, J. Electrical Influence Machines.i2mo, 2 00 

-Marine Boiler Design.i2mo, *1 25 

Greenhill, G. Dynamics of Mechanical Flight. 8 vo, *2 50 

Greenwood, E. Classified Guide to Technical and Commercial Books. 8vo, *3 00 

Gregorius, R. Mineral Waxes. Trans, by C. Salter.i2mo, *3 00 

Griffiths, A. B. A Treatise on Manures.i2mo, 3 00 

-Dental Metallurgy.8vo, *3 50 

Gross, E. Hops.8vo, *4 50 

Grossman, J. Ammonia and Its Compounds.i2mo, *1 25 

Groth, L. A. Welding and Cutting Metals by Gases or Electricity. 

(Westminster Series).8vo, *2 00 

Grover, F. Modern Gas and Oil Engines.8vo, *2 00 

Gruner, A. Power-loom Weaving.8vo, *3 00 

Guldner, Hugo. Internal Combustion Engines. Trans, by H. Diederichs. 

4to, *10 00 

Gunther, C. 0 . Integration.nmo, *1 25 

Gurden, R. L. Traverse Tables.folio, half morocco, *750 

Guy, A. E. Experiments on the Flexure of Beams.8vo, *1 25 

Haeder, H. Handbook on the Steam-engine. Trans, by H. H. P. 

Powles.nmo, 3 00 

Hainbach, R. Pottery Decoration. Trans, by C. Salter.nmo, *3 00 

Haenig, A. Emery and Emery Industry.8vo, *2 50 

Hale, W. J. Calculations of General Chemistry.nmo, *1 00 

Hall, C. H. Chemistry of Paints and Paint Vehicles.nmo, *2 00 

Hall, G. L. Elementary Theory of Alternate Current Working. .. .8vo, *i 50 

Hall, R. H. Governors and Governing Mechanism.nmo, *2 00 

Hall, W. S. Elements of the Differential and Integral Calculus.8vo, *2 25 

-Descriptive Geometry.8vo volume and a 4to atlas, *3 50 

Haller, G. F., and Cunningham, E. T. The Tesla Coil.nmo, *1 25 

Halsey, F. A. Slide Valve Gears.nmo, 1 50 

-The Use of the Slide Rule. (Science Series No. 114.).i6mo, o 50 

-Worm and Spiral Gearing. (Science Series No. 116.).i6mo, o 50 

Hamilton, W. G. Useful Information for Railway Men.i6mo, 1 00 

Hammer, W. J. Radium and Other Radio-active Substances.8vo, *1 00 

Hancock, H. Textbook of Mechanics and Hydrostatics.8vo, 1 50 

Hancock, W. C. Refractory Materials. (Metallurgy Series.) (In Press.) 

Hardy, E. Elementary Principles of Graphic Statics.12 mo, *1 50 

Harris, S. M. Practical Topographical Surveying. (In Press.) 

Harrison, W. B. The Mechanics’ Tool-book.nmo, 1 50 

Hart, J. W. External Plumbing Work.8vo, *3 00 

-Hints to Plumbers on Joint Wiping.8vo, *3 00 

-Principles of Hot Water Supply.8vo. *3 00 

-Sanitary Plumbing and Drainage.8vo, *3 00 











































D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 


Haskins, C. H. The Galvanometer and Its Uses.i6mo, 

Hatt, J. A. H. The Colorist.square i2mo, 

Hausbrand, E. Drying by Means of Air and Steam. Trans, by A. C. 

Wright.12 mo, 

-Evaporating, Condensing and Cooling Apparatus. Trans, by A. C. 

Wright.8vo, 

Hausner, A. Manufacture of Preserved Foods and Sweetmeats. Trans. 

by A. Morris and H. Robson.8vo, 

Hawke, W. H. Premier Cipher Telegraphic Code.4to, 

-100,000 Words Supplement to the Premier Code.4to, 

Hawkesworth, J. Graphical Handbook for Reinforced Concrete Design. 

4to, 

Hay, A. Alternating Currents.8vo, 

-Electrical Distributing Networks and Distributing Lines.8vo, 

-Continuous Current Engineering. 8vo, 

Hayes, H. V. Public Utilities, Their Cost New and Depreciation.. .8vo, 

Heap, Major D. P. Electrical Appliances.8vo, 

Heather, H. J. S. Electrical Engineering.8vo, 

Heaviside, O. Electromagnetic Theory. Vols. I and II . . . 8vo, each, 

Vol. Ill.8vo, 

Heck, R. C. H. The Steam Engine and Turbine.8vo, 

-Steam-Engine and Other Steam Motors. Two Volumes. 

Vol. I. Thermodynamics and the Mechanics.8vo, 

Vol. II. Form, Construction, and Working.8vo, 

-Notes on Elementary Kinematics.8vo, boards, 

-Graphics of Machine Forces.8vo, boards, 

Hedges, K. Modern Lightning Conductors.8vo, 

Heermann, P. Dyers’ Materials. Trans, by A. C. Wright.nmo, 

Hellot, Macquer and D’Apligny. Art of Dyeing Wool, Silk and Cotton. 8vo, 

Henrici, O. Skeleton Structures.8vo, 

Hering, D. W. Essentials of Physics for College Students.8vo, 

Hering-Shaw, A. Domestic Sanitation and Plumbing. Two V ols... 8vo, 

Hering-Shaw, A. Elementary Science.8vo, 

Herrmann, G. The Graphical Statics of Mechanism. Trans, by A. P. 

Smith.i2mo, 

Herzfeld, J. Testing of Yarns and Textile Fabrics.8vo, 

Hildebrandt, A. Airships, Past and Present.8vo, 

Hildenbrand, B. W. Cable-Making. (Science Series No. 32.)-i6mo, 

Hilditch, T. P. A Concise History of Chemistry.12010, 

Hill, T. W. The Purification of Public Water Supplies. New Edition. 

(In Press.)' 

-Interpretation of Water Analysis. (In Press.) 

Hill, M. J. M. The Theory of Proportion.8vo, 

Hiroi, I. Plate Girder Construction. (Science Series No. 95.) . .. i6mo, 
-Statically-Indeterminate Stresses.12010, 

Hirshfeld, C. F. Engineering Thermodynamics. (Science Series No. 45.) 

i6mo, 

Hobart, H. M. Heavy Electrical Engineering. 8vo, 

-Design of Static Transformers.12010, 

-Electricity. 8v0 * 

-Electric Trains. 8v0 > 


: 3 

1 50 

*1 50 

*2 00 

*5 00 

*3 00 
*5 00 
*5 00 

*2 50 
*2 50 
*3 5o 
*2 50 
*2 00 

2 00 
*3 50 
*5 00 
*7 50 
*5 00 

*3 50 
*5 00 
*1 00 
*1 00 

3 00 
*2 50 
*2 00 

1 50 
*1 75 
*5 00 
*2 00 

2 00 
*3 55 
*3 50 

o 50 
*1 25 


*2 50 
o 50 
*2 00 

o 50 
*4 50 
*2 00 
*2 00 
*2 50 








































I 4 D. VAN.NOSTRAND CO.’S SHORT TITLE CATALOG 


Hobart, H. M. Electric Propulsion of Ships.8vo, 

Hobart, J. F. Hard Soldering, Soft Soldering and Brazing.i2mo, 

Hobbs, W. R. P. The Arithmetic of Electrical Measurements... .i2mo, 

Hoft, J. N. Paint and Varnish Facts and Formulas.i2mo, 

Hole, W. The Distribution of Gas.8vo, 

Holley, A. L. Railway Practice.folio, 

Holmes, A. B. The Electric Light Popularly Explained. ..i2mo, paper, 

Hopkins, N. M. Experimental Electrochemistry.8vo, 

-Model Engines and Small Boats.i2mo, 

Hopkinson, J., Shoolbred, J. N., and Day, R. E. Dynamic Electricity. 

(Science Series No. 71.).i6mo, 

Horner, J. Metal Turning.nmo, 

-Practical Ironfounding. 8vo, 

-Plating and Boiler Making.8vo, 

-Gear Cutting, in Theory and Practice.8vo, 

Houghton, C. E. The Elements of Mechanics of Materials.xamo, 

Houllevigue, L. The Evolution of the Sciences.8vo, 

Houstoun, R. A. Studies in Light Production.i2mo, 

Hovenden, F. Practical Mathematics for Young Engineers.nmo, 

Howe, G. Mathematics for the Practical Man.i2mo, 

Howorth, J. Repairing and Riveting Glass, China and Earthenware. 

8vo, paper, 

Hubbard, E. The Utilization of Wood-waste.8vo, 

Hiibner, J. Bleaching and Dyeing of Vegetable and Fibrous Materials. 

(Outlines of Industrial Chemistry.).8vo, *5 00 

Hudson, 0 . F. Iron and Steel. (Outlines of Industrial Chemistry.).8vo, *2 00 

Humper, W. Calculation of Strains in Girders.i2mo, 2 50 

Humphrey, J. C. W. Metallography of Strain. (Metallurgy Series.) 

(In Press.) 

Humphreys, A. C. The Business Features of Engineering Practice..8vo, *1 25 

Hunter, A. Bridge Work.8vo. (In Press.) 

Hurst, G. H. Handbook of the Theory of Color. .8vo, *2 50 

-Dictionary of Chemicals and Raw Products.8vo, *3 00 

-Lubricating Oils, Fats and Greases.8vo, *4 00 

-Soaps.8vo, 

Hurst, G. H., and Simmons, W. H. Textile Soaps and Oils.8vo, 

Hurst, H. E., and Lattey, R. T. Text-book of Physics.8vo, 

-Also published in three parts. 

Part I. Dynamics and Heat. *1 25 

Part II. Sound and Light. *1 25 

Part* III. Magnetism and Electricity. *1 50 

Hutchinson, R. W., Jr. Long Distance Electric Power Transmission. 

i2mo, *3 00 

Hutchinson, R. W., Jr., and Thomas, W. A. Electricity in Mining. i2ino, 

(In Press.) 



*2 

OO 


*1 

OO 

.. i2mo, 

0 

50 


*1 

50 

... . 8vo, 

*7 

50 

.. .folio, 

12 

OO 

, paper, 

0 

50 

... . 8vo, 

*3 

00 


1 

25 

ctricity. 

. . i6mo, 

0 

50 

. . i2mo, 

1 

53 


*2 

00 


3 

00 

.. . 8vo, 

*3 

CD 

. . i2mo, 

*2 

CD 

.. . 8vo, 

*2 

00 

. . i2mo, 

2 

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. . i2mo, 

*1 

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.. i2mo, 

*! 

25 

enware. 

, paper, 

*0 

50 

... 8vo, 

*2 

50 


*5 00 
*2 50 
*3 00 


Hutchinson, W. B. Patents and How to Make Money Out of Them. 

i2mo, 1 25 


Hutton, W. S. Steam-boiler Construction.8vo, 6 00 

-Practical Engineer’s Handbook...8vo, 7 00 

-The Works’ Manager’s Handbook...8vo, 6 00 



































D VAN NOSTRAND CO.’S SHORT TITLE CATALOG 


15 


Hyde, E. W. Skew Arches. (Science Series No. 15.).i6mo, o 50 

Hyde, F. S. Solvents, 0 . 1 s, Gums, Waxes.8vo, *2 00 


Induction Coils. (Science Serbs No. 53.).i6mo, 

Ingham, A. E. Gearing. A practical treatise.8vo, 

Ingle, H. Manual of Agricultural Chemistry.8vo, 

Inness, C. H. Problems in Machine Design.i2mo, 

-Air Compressors and Blowing Engines.12mo, 

-Centrifugal Pumps..121210, 

-The Fan.i2mo, 

Isherwood, B. F. Engineering Precedents for Steam Machinery. . .8vo, 
Ivatts, E. B. Railway Management at Stations.8vo, 


Jacob, A., and Gould, E. S. On the Designing and Construction of 

Storage Reservoirs. (Science Series No. 6).i6mo, 

Jannettaz, E. Guide to the Determination of Rocks. Trans, by G. W. 

Plympton.i2mo, 

Jehl, F. Manufacture of Carbons.8vo, 

Jennings, A. S. Commercial Paints and Painting. (Westminster Series.) 

8vo, 

Jennison, F. H. The Manufacture of Lake Pigments.8vo, 

Jepson, G. Cams and the Principles of their Construction.8vo, 

-Mechanical Drawing.8vo {In Preparation.} 

Jockin, W. Arithmetic of the Gold and Silversmith.i2mo, 

Johnson, J. H. Arc Lamps and Accessory Apparatus. (Installation 

Manuals Series.).i2mo, 

Johnson, T. M. Ship Wiring and Fitting. (Installation Manuals Series.) 

i2mo, 

Johnson, W. H. The Cultivation and Preparation of Para Rubber. . 8vo, 

Johnson, W. McA. The Metallurgy of Nickel. {In Preparation.) 

Johnston, J. F. W., and Cameron, C. Elements of Agricultural Chemistry 

and Geology.nmo, 

Joly, J. Radioactivity and Geology. i2mo, 

Jones, H. C. Electrical Nature of Matter and Radioactivity.i2mo, 

-New Era in Chemistry..12010, 

Jones, M. W. Testing Raw Materials Used in Paint.i2mo, 

Jones, L., and Scard, F. I. Manufacture of Cane Sugar.8vo, 

Jordan, L. C. Practical Railway Spiral.i2mo, leather, 

Toynson, F. H. Designing and Construction of Machine Gearing . 8vo, 
Jiiptner, H. F. V. Siderology: The Science of Iron.8vo, 


Kansas City Bridge. 4 * 0 , 

Kapp, G. Alternate Current Machinery. (Science Series No. 96.).i6mo, 

Keim, A. W. Prevention of Dampness in Buildings.8vo, 

Keller, S. S. Mathematics for Engineering Students. 12010, half leather. 

Algebra and Trigonometry, with a Chapter on Vectors. 

Special Algebra Edition. 

Plane and Solid Geometry. 

Analytical Geometry and Calculus. 

Kelsey, W. R. Continuous-current Dynamos and Motors.8vo, 

Kemble, W. T., and Underhill, C. R. The Periodic Law and the Hydrogen 
Spectrum.8vo, paper, 


o 53 
*2 50 

*3 00 
*2 00 
*2 00 
*2 00 
*2 00 
2 50 
*2 50 


o 50 

1 5o 
*4 00 

*2 00 
*3 co 
*1 50 

*1 00 

*0 75 

*0 75 
*3 co 


2 60 

3 00 
*2 00 
*2 00 

*2 00 
*5 00 

*1 50 
2 00 
*5 00 

6 00 
o 50 
*2 00 

*1 75 
*1.00 
*1.25 
*2 00 
*2 50 

*0 50 






































16 D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 

Kemp, J. F. Handbook of Rocks.8vo, *i 50 

Kendall, E. Twelve Figure Cipher Code. 4 to > * 12 5 <> 

Kennedy, A. B. W., and Thurston, R. H. Kinematics of Machinery. 

(Science Series No. 54.)..i6mo, o 50 

Kennedy, A. B. W., Unwin, W. C., and Idell, F. E. Compressed Air. 

(Science Series No. 106.).i6mo, o 50 

Kennedy, R. Modern Engines and Power Generators. Six Volumes. 4to, 15 00 

Single Volumes.each, 3 00 

-Electrical Installations. Five Volumes.4to, 15 00 

Single Volumes.each, 3 50 

-Flying Machines; Practice and Design.i2mo, *2 00 

-Principles of Aeroplane Construction.8vo, *1 50 

Kennedy, A. E. Electro-dynamic Machinery.8vo, 1 50 

Kent, W. Strength of Materials. (Science Series No. 41.).i6mo, o 50 

Kershaw, J. B. C. Fuel, Water and Gas Analysis.8vo, *2 50 

-Electrometallurgy. (Westminster Series.).8vo, *200 

-The Electric Furnace in Iron and Steel Production.i2mo, *1 50 

-Electro-Thermal Methods of Iron and Steel Production. .. .8vo, *3 00 

Kinzbrunner, C. Alternate Current Windings..8vo, *1 50 

-Continuous Current Armatures. .8vo, *1 50 

-Testing of Alternating Current Machines.8vo, *2 00 

Kirkaldy, W. G. David Kirkaldy’s System of Mechanical Testing. .4to, 10 00 

Kirkbride, J. Engraving for Illustration.8vo, *1 50 

Kirkwood, J. P. Filtration of River Waters.4to, 7 50 

Kirschke, A. Gas and Oil Engines.i2mo, *1 25 

Klein, J. F. Design of a High-speed Steam-engine.8vo, *5 00 

-Physical Significance of Entropy.8vo, *1 50 

Kleinhans, F. B. Boiler Construction.8vo, 3 00 

Knight, R.-Adm. A. M. Modern Seamanship.8vo, *7 50 

Half morocco. *9 00 

Knox, J. Physico-Chemical Calculations.i2mo, *1 00 

-Fixation of Atmospheric Nitrogen. (Chemical Monographs, 

No. 4.).i2mo, *0 75 

Knox, W. F. Logarithm Tables. (In Preparation.) 

Knott, C. G., and Mackay, J. S. Practical Mathematics.8vo, 2 00 

Koester, F. Steam-Electric Power Plants.4to, *5 00 

-Hydroelectric Developments and Engineering.4to, *5 00 

Koller, T. The Utilization of Waste Products.8vo, *3 50 

-Cosmetics.8vo, *2 50 

Kremann, R. Application of the Physico-Chemical Theory to Tech¬ 
nical Processes and Manufacturing Methods. Trans, by H. 

E. Potts.8vo, *2 50 

Kretchmar, K. Yarn and Warp Sizing.8vo, *4 00 

Lallier, E. V. Elementary Manual of the Steam Engine.i2mo, *2 00 

Lambert, T. Lead and Its Compounds.8vo, *3 50 

-Bone Products and Manures.8vo, *3 00 

Lamborn, L. L. Cottonseed Products.8vo, *3 00 

-Modern Soaps, Candles, and Glycerin.8vo, *7 50 

Lamprecht, R. Recovery Work After Pit Fires. Trans, by C. Salter. 8vo, *4 00 

Lancaster, M. Electric Heating, Cooking and Cleaning.8vo, *1 50 




















































D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG \y 

Lanchester, F. W. Aerial Flight. Two Volumes. 8vo. 

Vol. I. Aerodynamics. *6 oo 

-Aerial Flight. Vol. II. Aerodonetics. *6.00 

Larner, E. T. Principles of Alternating Currents.i2mo. *1 25 

Larrabee, C. S. Cipher and Secret Letter and Telegraphic Code. i6mo, o 60 

La Rue, B. F. Swing Bridges. (Science Series No. 107.).i6mo, o 50 

Lassar-Cohn. Dr. Modern Scientific Chemistry. Trans, by M. M. 

Pattison Muir.i2mo, *2 00 

Latimer, L. H., Field, C. J., and Howell, J. W. Incandescent Electric 

Lighting. (Science Series No. 57.) .i6mo, o 50 

Latta, M. N. Handbook of American Gas-Engineering Practice . . 8vo, *4 50 

-American Producer Gas Practice.4to, *6 00 

Laws, B. C. Stability and Equilibrium of Floating Bodies.8vo, *3 50 

Lawson, W. R. British Railways. A Financial and Commercial 

Survey.•.8vo, 2 00 

Leask, A. R. Breakdowns at Sea.i2mo, 200 

-Refrigerating Machinery.i2mo, 200 

Lecky, S. T. S. “ Wrinkles ” in Practical Navigation.8vo, *8 00 

Le Doux, M. Ice-Making Machines. (Science Series No. 46.). . i6mo, o 50 

Leeds, C. C. Mechanical Drawing for Trade Schools.oblong 4to, 

High School Edition. *1 25 

Machinery Trades Edition. *2.00 

Lefevre, L. Architectural Pottery. Trans, by H. K. Bird and W. M. 

Binns.... A'...4to, *7 50 

Lehner, S. Ink Manufacture. Trans, by A. Morris and H. Robson. 8vo, *2 50 

Lemstrom, S. Electricity in Agriculture and Horticulture.8vo, *1 50 

Letts, E. A. Fundamental Problems in Chemistry.8vo, *2 00 

Le Van, W. B. Steam-Engine Indicator. (Science Series No. 78.)i6mo, 0 50 

Lewes, V. B. Liquid and Gaseous Fuels. (Westminster Series.). .8vo, *200 

-Carbonization of Coal.8vo, *3 00 

Lewis, L. P. Railway Signal Engineering.8vo, *3 50 

Lieber, B. F. Lieber’s Standard Telegraphic Code.8vo, *10 00 

-Code. German Edition.8vo, *10 00 

-Spanish Edition.8vo, *10 00 

-French Edition.8vo, *10 00 

-Terminal Index.8vo, *2 50 

-Lieber’s Appendix.folio, *15 00 

-Handy Tables.4to, *2 50 

-Bankers and Stockbrokers’ Code and Merchants and Shippers’ 

Blank Tables.8vo, *15 00 

-100,000,000 Combination Code.8vo, *10 00 

-Engineering Code.8vo, *12 50 

Livermore, V. P., and Williams, J. How to Become a Competent Motor- 

man.i2mo, *1 00 

Liversedge, A. J. Commercial Engineering.8vo, *300 

Livingstone, R. Design and Construction of Commutators.8vo, *2 25 

-Mechanical Design and Construction of Generators.8vo, *3 50 

Lobben, P. Machinists’ and Draftsmen’s Handbook.8vo, 2 50 

Lockwood, T. D. Electricity, Magnetism, and Electro-telegraph 8vo, 2 50 











































18 D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 


Lockwood, T. D. Electrical Measurement and the Galvanometer. 

i2mo, o 75 

Lodge, O. J. Elementary Mechanics.i2mo, i 50 

—— Signalling Across Space without Wires.8vo, *2 00 

Loewenstein, L. C., and Crissey, C. P. Centrifugal Pumps. *4 50 

Lord, R. T. Decorative and Fancy Fabrics.8vo, *3 50 

Loring, A. E. A Handbook of the Electromagnetic Telegraph .... i6mo o 50 

-Handbook. (Science Series No. 39.).i6mo, o 50 

Low, D. A. Applied Mechanics (Elementary).i6mo, o So 

Lubschez, B. J. Perspective.i2mo, *1 50 

Lucke, C. E. Gas Engine Design.8vo, *3 00 

-Power Plants: Design, Efficiency, and Power Costs. 2 vols. 

(In Preparation.) 

Lunge, G. Coal-tar and Ammonia. Two Volumes.8vo, *15 00 

-Manufacture of Sulphuric Acid and Alkali. Four Volumes.... 8vo, 

Vol. I. Sulphuric Acid. In three parts.*18 co 

Vol. II. Salt Cake, Hydrochloric Acid and Leblanc Soda. In two 

parts..*15.00 

Vol. III. Ammonia Soda.*10 on 

Vol. IV. Electrolytic Methods. (In Press.) 

— — Technical Chemists’ Handbook.i2mo, leather, *3 50 

-Technical Methods of Chemical Analysis. Trans, by C. A. Keane 

in collaboration with the corps of specialists. 

Vol. I. In two parts.8vo, *15 00 

Vol. II. In two parts.8vo, *18 00 

Vol. Ill. (In Preparation.) 

Lupton, A., Parr, G. D. A., and Perkin, H. Electricity as Applied to 

Mining.8vo, *4 50 

Luquer, L. M. Minerals in Rock Sections.8vo, *1 50 


Macewen, H. A. Food Inspection.8vo, 

Mackenzie, N. F. Notes on Irrigation Works.8vo, 

Mackie, J. How to Make a Woolen Mill Pay.8vo, 

Mackrow, C. Naval Architect’s and Shipbuilder’s Pocket-book. 

i6mo, leather, 

Maguire, Wm. R. Domestic Sanitary Drainage and Plumbing . . . .8vo, 
Mallet, A. Compound Engines. Trans, by R. R. Buel. (Science Series 

No. 10.).i6mo, 

Mansfield, A. N. Electro-magnets. (Science Series No. 64.) . . . i6mo, 
Marks, E. C. R. Construction of Cranes and Lifting Machinery . i2mo, 

-Construction and Working of Pumps.i2mo, 

-Manufacture of Iron and Steel Tubes.i2mo, 

-Mechanical Engineering Materials.i2mo, 

Marks, G. C. Hydraulic Power Engineering.8vo, 

-Inventions, Patents and Designs.i2mo, 

Marlow, T. G. Drying Machinery and Pr: ctice.8vo, 

Marsh, C. F. Concise Treatise on Reinforced Concrete .8vo, 


-Reinforced Concrete Compression Member Diagram. Mounted on 

Cloth Boards . 


*2 50 
*2 50 
*2 00 

5 00 
4 00 


o 50 
*1 50 
*1 50 
*2 00 
*1 00 
3 50 
*1 00 
*5 00 
*2 50 

*1.50 

































D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 


Marsh, C. F., and Dunn, W. Manual of Reinforced Concrete and Con¬ 
crete Block Construction.i6mo, morocco, 

Marshall, W. J., and Sankey, H. R. Gas Engines. (Westminster Series.) 

8 vo, 

Martin, G. Triumphs and Wonders of Modern Chemistry.8vo, 

Martin, N. Properties and Design of Reinforced Concrete.nmo, 

Martin, W. D. Hints to Engineers..i2mo, 

Massie, W. W., and Underhill, C. R. Wireless Telegraphy and Telephony. 

i2mo, 

Matheson,D. Australian Saw-Miller’s Log and Timber Ready Reckoner. 

i2mo, leather, 


Mathot, R. E. Internal Combustion Engines.8vo, 

Maurice, W. Electric Blasting Apparatus and Explosives.8vo, 

•-Shot Firer’s Guide.. 8vo, 

Maxwell, J. C. Matter and Motion. (Science Series No. 36.). 

i6mc, 

Maxwell, W. H., and Brown, J. T. Encyclopedia of Municipal and Sani¬ 
tary Engineering.4to, * 

Mayer, A. M. Lecture Notes on Physics.8vo, 

McCullough, R. S. Mechanical Theory of Heat.8vo, 

McGibbon, W. C. Indicator Diagrams for Marine Engineers.8vo, 

-Marine Engineers’ Drawing Book.oblong 4to, 

McIntosh, J. G. Technology of Sugar.8vo, 


Industrial Alcohol.8vo, 

Manufacture of Varnishes and Kindred Industries. Three Volumes. 
8vo. 


Vol. I. Oil Crushing, Refining and Boiling. 

Vol. II. Varnish Materials and Oil Varnish Making. 

Vol. III. Spirit Varnishes and Materials. 

McKnight, J. D., and Brown, A. W. Marine Multitubular Boilers. 

McMaster, J. B. Bridge and Tunnel Centres. (Science Series No. 20.) 

i6mo, 

McMechen, F. L. Tests for Ores, Minerals and Metals.i2mo, 

McPherson, J. A. Water-works Distribution.8vo, 

Melick, C. W. Dairy Laboratory Guide.i2mo, 

Merck, E. Chemical Reagents; Their Purity and Tests. Trans, by 

H. E. Schenck...8vo, 

Merivale, J. H. Notes and Formulae for Mining Students.i2mo, 


Merritt, Wm. H. Field Testing for Gold and Silver.i6mo, leather, 

Messer, W. A. Railway Permanent Way.8vo {In Press.) 

Meyer, J. G. A., and Pecker, C. G. Mechanical Drawing and Machine 

Design. 41 °> 

Michell, S. Mine Drainage.8vo, 

Mierzinski, S. Waterproofing of Fabrics. Trans, by A. Morris and H. 

Robson. 8vo, 

Miller, G. A. Determinants. (Science Series No 105.).i6mo, 

Milroy, M. E. W. Home Lace-making.i2mo, 

Minifie, W. Mechanical Drawing.8vo, 

Mitchell, C. A. Mineral and Aerated Waters.8vo, 


19 


*2 50 

*2 00 
*2 00 
*2 50 

*1 00 
*1 00 

1 50 
*6 co 
*3 50 

*1 50 

o 50 

10 00 

2 00 

3 50 
*3 00 

*2 00 

*4 50 
*3 00 


*3 50 
*4 00 
*4 50 

*1 50 

o 50 
*1 00 
2 50 
*1 25 

1 00 

1 50 
1 50 


5 00 
10 00 

*2 50 

*1 00 
*4 00 
*3 00 




































20 


D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 


Mitchell, C. A., and Prideaux, R. M. Fibres Used in Textile and Allied 

Industries.8vo, *3 co 

Mitchell, C. F., and G. A. Building Construction and Drawing. i2mo. 

Elementary Course. *1 50 

Advanced Course. *2 50 

Monckton, C. C. F. Radiotelegraphy. (Westminster Series.).8vo, *200 

Monteverde, R. D. Vest Pocket Glossary of English-Spanish, Spanish- 

English Technical Terms.64m©, leather, *1 00 

Montgomery, J. H. Electric Wiring Specifications. (In Press.) 

Moore, E. C. S. New Tables for the Complete Solution of Ganguillet and 

Kutter’s Formula.8vo, *500 

Morecroft, J. H., and Hehre, F. W. Short Course in Electrical Testing. 

8vo, *1 50 

Moreing, C. A., and Neal, T. New General and Mining Telegraph Code. 


8vo, *5 00 

Morgan, A. P. Wireless Telegraph Apparatus for Amateurs.i2mo, *1 50 

Moses, A. J. The Characters of Crystals.8vo, *2 00 

-and Parsons, C. L. Elements of Mineralogy.8vo, *2 50 

Moss, S.A. Elements of Gas Engine Design.(Science Series No.i2i.)i6mo, o 50 

-The Lay-out of Corliss Valve Gears. (Science Series No. 119.) i6mo, o 50 

Mulford, A. C. Boundaries and Landmarks.i2mo, *1 00 

Mullin, J. P. Modern Moulding and Pattern-making.i2mo, 2 50 

Munby, A. E. Chemistry and Physics of Building Materials. (West¬ 
minster Series.).8vo, *2 00 

Murphy, J. G. Practical Mining.i6mo, 1 00 

Murphy, W. S. Textile Industries. Eight Volumes. *20 00 

Sold separately, each, *3 00 

Murray, J. A. Soils and Manures. (Westminster Series.).8vo, *2 00 

Naquet, A. Legal Chemistry.i2mo, 200 

Nasmith, J. The Student’s Cotton Spinning.8vo, 3 00 

-Recent Cotton Mill Construction.i2mo, 2 00 

Neave, G. B., and Heilbron, I. M. Identification of Organic Compounds. 

i2mo, *1 25 

Neilson, R. M. Aeroplane Patents.8vo, *200 

Nerz, F. Searchlights. Trans, by C. Rodgers.8vo, *3 00 

Neuberger, H., and Noalhat, H. Technology of Petroleum. Trans, by 

J. G. McIntosh.8vo, *10 00 

Newall, J. W. Drawing, Sizing and Cutting Bevel-gears.8vo, 1 50 

Nicol, G. Ship Construction and Calculations.8vo, *4 50 

Nipher, F. E. Theory of Magnetic Measurements.i2mo, 1 00 

Nisbet, H. Grammar of Textile Design.8vo, *3 00 

Nolan, H. The Telescope. (Science Series No. 51.).i6mo, 050 

Noll, A. How to Wire Buildings.i2mo, 1 50 

North, H. B. Laboratory Experiments in General Chemistry.12010, *1 00 

Nugent, E. Treatise on Optics.12010, 1 50 

O’Connor, H. The Gas Engineer’s Pocketbook.i2mo, leather, 350 

■-Petrol Air Gas.12010, *0 75 



































D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 21 

Ohm, G. S., and Lockwood, T. D. Galvanic Circuit. Translated by 

William Francis. (Science Series No. 102.).i6mo, o 50 

Olsen, J. C. Text-book of Quantitative Chemical Analysis.8vo, *4 00 

Olsson, A. Motor Control, in Turret Turning and Gun Elevating. (U. S. 

Navy Electrical Series, No. 1.).i2mo, paper, *0 50 

Ormsby, M. T. M. Surveying.i2mo, 1 50 

Oudin, M. A, Standard Polyphase Apparatus and Systems.8vo, *3 00 

Cwen, D. Recent Physical Research...8vo, *1 50 

Pakes, W. C. C., and Nankivell, A. T. The Science of Hygiene . . 8 vo, *1 75 

Palaz, A. Industrial Photometry. Trans, by G. W. Patterson, Jr. . 8vo, *4 00 

Pamely, C. Colliery Manager’s Handbook.8vo, *10 00 

Parker, P. A. M. The Control of Water.8vo, *5 00 

Parr, G. D. A. Electrical Engineering Measuring Instruments. .. .8vo, *3 50 
Parry, E. J. Chemistry of Essential Oils and Artificial Perfumes.. 8vo, *5 00 

-Foods and Drugs. Two Volumes.8vo, 

Vol. I. Chemical and Microscopical Analysis of Foods and Drugs. *7 5 ° 

Vol. H. Sale of Food and Drugs Act. *3 00 

-and Coste, J. H. Chemistry of Pigments. 8vo, *4 5a 

Parry, L. A. Risk and Dangers of Various Occupations.8vo, *3 00 

Parshall, H. F., and Hobart, H. M. Armature Windings.4to, *750 

-Electric Railway Engineering.4to, *10 00 

-and Parry, E. Electrical Equipment of Tramways.. {In Press.) 

Parsons, S. J. Malleable Cast Iron.8vo, *2 50 

Partington, J. R. Higher Mathematics for Chemical Students. .i2mo, *2 00 

-Textbook of Thermodynamics.8vo, *4 00 

Passmore, A. C. Technical Terms Used in Architecture.8vo, *3 50 

Patchell, W. H. Electric Power in Mines.8vo, *4 00 

Paterson, G. W. L. Wiring Calculations.i2mo, *2 00 

Patterson, D. The Color Printing of Carpet Yarns.8vo, *3 50 

-Color Matching on Textiles.8vo, *3 00 

-The Science of Color Mixing.8vo, *3 00 

Paulding, C. P. Condensation of Steam in Covered and Bare Pipes. .8vo, *2 00 

-Transmission of Heat through Cold-storage Insulation.12010, *1 00 

Payne, D. W. Iron Founders’ Handbook. (In Press.) 

Peddie, R. A. Engineering and Metallurgical Books.12010, *150 

Peirce, B. System of Analytic Mechanics.4to, 10 00 

Pendred, V. The Railway Locomotive. (Westminster Series.).8vo, *2 00 

Perkin, F. M. Practical Methods of Inorganic Chemistry.iamo, *1 00 

Perrigo, 0 . E. Change Gear Devices.8vo, 1 00 

Perrine, F. A. C. Conductors for Electrical Distribution.8vo, *3 50 

Perry, J. Applied Mechanics.8vo, *2 50 

Petit, G. White Lead and Zinc White Paints.8vo, *1 50 

Petit, R. How to Build an Aeroplane. Trans, by T. O’B. Hubbard, and 

J. H. Ledeboer.8vo, *150 

Pettit, Lieut. J. S. Graphic Processes. (Science Series No. 76.)... i6mo, 053 
Philbrick, P. H. Beams and Girders. (Science Series No. 88.)... i6mo, 

Phillips, J. Engineering Chemistry.8vo, *4 50 

-Gold Assaying.8vo, * 2 5 ° 

-Dangerous Goods.8vo, 3 50 









































22 


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-Logarithms for Beginners.i2mo. boards, o 50 

-The Slide Rule.12 mo, ’ 1 00 

Plattner’s Manual of Blow-pipe Analysis. Eighth Edition, revised. Trans. 

by H. B. Cornwall.8vo, *4 00 

Pl7mpton, G. W. The Aneroid Barometer. (Science Series No. 35.) i6mo, o 50 

-How to become an Engineer. (Science Series No. 100.).i6mo, o 50 

-Van Nostrand’s Table Book. (Science Series No. 104.).i6mo, o 50 

Fochet, M. L. Steam Injectors. Translated from the French. (Science 

Series No. 29.). i6mo, o 50 

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leather, 1 00 

Polleyn, F. Dressings and Finishings for Textile Fabrics.8vo, *3 00 

Pope, F. G. Organic Chemistry.i2mo, *2 25 

Pope, F. L. Modern Practice of the Electric Telegraph.8vo, 1 50 

Popple well, W. C. Elementary Treatise on Heat and Heat Engines . i2mo, *3 00 

—'— Prevention of Smoke.8vo, *3 50 

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Porritt, B. D. The Chemistry of Rubber. (Chemical Monographs, 

No. 3.).i2mo, *075 

Porter, J. R. Helicopter Flying Machine.12010, *1 25 

Potter, T. Concrete.8vo, *3 co 

Potts, H. E. Chemistry of the Rubber Industry. (Outlines of Indus¬ 
trial Chemistry).... .8vo, *2 00 

Practical Compounding of Oils, Tallow and Grease. 8vo, *3 50 

Practical Iron Founding.12010, 1 50 

Pratt, K. Boiler Draught. 12010, *1 25 

Pray, T., Jr. Twenty Years with the Indicator.8vo, 2 50 

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Preece, W. H. Electric Lamps. (In Press.) 

Prelini, C. Earth and Rock Excavation.8vo, *3 00 

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-Tunneling. New Edition.8vo, *3 00 

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Prescott, A. B., and Johnson, 0 . C. Qualitative Chemical Analysis. . . 8vo, *3 50 

Prescott, A. B., and Sullivan, E. C. First Book in Qualitative Chemistry. 

I 2 ffiO, *1 50 

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Pritchard, 0 . G. The Manufacture of Electric-light Carbons . 8vo, paper, *0 60 
Pullen, W. W. F. Application of Graphic Methods to the Design of 

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Pulsifer, W. H. Notes for a History of Lead.8vo, 4 00 

Purchase, W. R. Masonry.nmo, *3 00 

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Pynchon, T. R. Introduction to Chemical Physics...8vo, 3 oo 








































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Rafter, G. W., and Baker, M. N. Sewage Disposal in the United States. 

4to, 

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Randall, P. M. Quartz Operator’s Handbook.12mo, 

Randau, P. Enamels and Enamelling.8vo, 

Rankine, W. J. M. Applied Mechanics.8vo, 

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Rankine, W. J. M., and Bamber, E. F. A Mechanical Text-book_8vo, 

Raphael, F. C. Localization of Faults in Electric Light and Power Mains. 

8vo, 


Rasch, E. Electric Arc Phenomena. Trans, by K. Tornberg.8vo, 

Rathbone, R. L. B. Simple Jewellery.8vo, 

Rateau, A. Flow of Steam through Nozzles and Orifices. Trans, by H. 

B. Brydon.8vo 

Rausenberger, F. The Theory of the Recoil of Guns.8vo, 

Rautenstrauch, W. Notes on the Elements of Machine Design.8vo, boards, 
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Raymond, E. B. Alternating Current Engineering.nmo, 

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oblong 4to, boards, 


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Reiser, F. Hardening and Tempering of Steel. Trans, by A. Morris and 

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23 

o 50 
o 50 
o 50 

*6 00 
*4 00 

2 00 
*4 00 

5 00 

6 50 
5 00 
5 00 
4 00 

3 5o 

*3 00 
*2 00 
*2 00 

*1 50 
*4 50 
*1 50 


*1 25 

*2 50 
*2 50 
*3 50 
*4 50 

*0 50 
*1 25 
o 50 
*5 00 
*5 00 
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1 00 
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24 D. VAN NOSTRAND CO.’S SHORT TITLE CATALOG 


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Rhead, G. F. Simple Structural Woodwork.i2mo, *100 

Rhodes, H. J. Art of Lithography.8vo, 3 50 

Rice, J. M., and Johnson, W. W. A New Method of Obtaining the Differ¬ 
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Richards, W. A., and North, H. B. Manual of Cement Testing.. . . i2mo, *1 50 

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Richardson, S. S. Magnetism and Electricity.nmo, *2 00 

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-Reinforced Concrete Bridges.4to, *5 00 

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Rogers, A. A Laboratory Guide of Industrial Chemistry.121110, *1 50 

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8vo, (In Press.) 

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Roth. Physical Chemistry.8vo, *2 00 

Rouillion, L. The Economics of Manual Training.8vo, 2 00 

Rowan, F. J. Practical Physics of the Modern Steam-boiler.8vo, *3 00 

-and Idell, F. E. Boiler Incrustation and Corrosion. (Science 

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Roxburgh, W. General Foundry Practice. (Westminster Series.) .8vo, *2 03 

Ruhmer, E. Wireless Telephony. Trans, by J. Erskine-Murray.. 8vo, *350 
Russell, A. Theory of Electric Cables and Networks.8vo, *3 00 

Sabine, R. History and Progress of the Electric Telegraph.i2mo, 1 2*-, 

Saeltzer, A. Treatise on Acoustics.i2mo, 1 00 








































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Sanford, P. G. Nitro-explosives.8vo, *4 00 

Saunders, C. H. Handbook of Practical Mechanics.i6mo, 1 00 

leather, 1 25 

Saunnier, C. Watchmaker’s Handbook.i 2 mo, 3 00 

Sayers, H. M. Brakes for Tram Cars.8vo, *1 25 

Scheele, C. W. Chemical Essays.8vo, *2 00 

Scheithauer, W. Shale Oils and Tars.8vo, *3 5o 

Schellen, H. Magneto-electric and Dynamo-electric Machines .... 8vo, 5 oo 

Scherer, R. Casein. Trans, by C. Salter..8vo, *300 

Schidrowitz, P. Rubber, Its Production and Industrial Uses.8vo, *5 00 

Schindler, K. Iron and Steel Construction Works.i2mo, *1 25 

Schmall, C. N. First Course in Analytic Geometry, Plane and Solid. 

i2mo, half leather, *1 75 

Schmall, C. N., and Shack, S. M. Elements of Plane Geometry.. . i2mo, *1 25 

Schmeer, L. Flow of Water.8vo, *3 00 

Schumann, F. A Manual of Heating and Ventilation. .. .i2mo, leather, 1 50 

Schwarz, E. H. L. Causal Geology.8vo, *2 50 

Sehweizer, V. Distillation of Resins.8vo, *3 50 

Scott, W. W. Qualitative Analysis. A Laboratory Manual.8vo, *1 50 

Scribner, J. M. Engineers’ and Mechanics’ Companion. .i6mo, leather, 1 50 

Scuddeir, Electrical Conductivity and Ionization Constants of 

Organic Compounds.8vo, *3 00 

Searle, A. B. Modern Brickmaking.8vo, *5 00 

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Searle, G. M. “Sumners’ Method.” Condensed and Improved. 

(Science Series No. 124.).i6mo, o 50 

Seaton, A. E. Manual of Marine Engineering.8vo 8 00 

Seaton, A. E., and Rounthwaite, H. M. Pocket-book of Marine Engi¬ 
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Seeligmann, T., Torrilhon, G. L., and Falconnet, H. India Rubber and 

Gutta Percha. Trans, by J. G. McIntosh.8vo, *5 00 

Seidell, A. Solubilities of Inorganic and Organic Substances.8vo, *3 00 

Seligman, R. Aluminum. (Metallurgy Series.). (In Press.) 

Sellew, W. H. Steel Rails.4to, *12 50 

Senter, G. Outlines of Physical Chemistry.i2mo, *1 75 

-Text-book of Inorganic Chemistry.i2mo, *1 75 

Sever, G. F. Electric Engineering Experiments.8vo, boards, *1 00 

Sever, G. F., and Townsend, F. Laboratory and Factory Tests in Elec¬ 
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Sewall, C. H. Wireless Telegraphy.8vo, *2 00 

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Sewell, T. Elements of Electrical Engineering.8vo, *3 00 

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Sexton, A. H. Fuel and Refractory Materials.i2mo, *2 50 

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26 D. VAN NOSTRAND CO/S SHORT TITLE CATALOG 


Shaw, Henry S. H. Mechanical Integrators. (Science Series No. 83.) 

i6mo, o 50 

Shaw, S. History of the Staffordshire Potteries.8vo, 2 00 

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Shaw, W. N. Forecasting Weather.8vo, *3 50 

Sheldon, S., and Hausmann, E. Direct Current Machines.i2mo, *2 50 

-Alternating Current Machines.nmo, *2 50 

Sheldon, S., and Hausmann, E. Electric Traction and Transmission 

Engineering.i2mo, *2 50 

Sheriff, F. F. Oil Merchants’ Manual.12010, *3 50 

Shields, J. E. Notes on Engineering Construction.i2mo, 1 50 

Shreve, S. H. Strength of Bridges and Roofs...8vo, 3 50 

Shunk, W. F. The Field Engineer.iamo, morocco, 2 50 

Simmons, W. H., and Appleton, H. A. Handbook of Soap Manufacture, 

8vo, *3 00 

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Simms, F. W. The Principles and Practice of Levelling.8vo, 2 50 

-Practical Tunneling.8vo, 7 50 

Simpson, G. The Naval Constructor...i2mo, morocco, *500 

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Sinclair, A. Development of the Locomotive Engine.. .8vo, half leather, 5 00 

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Sindall, R. W., and Bacon, W. N. The Testing of Wood Pulp.8vo, *2 50 

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Sloane, T. O’C. Elementary Electrical Calculations.i2mo, *2 00 

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Snow, W. G., and Nolan, T. Ventilation of Buildings. (Science Series 

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Solomon, M. Electric Lamps. (Westminster Series.).8vo, *2 00 

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Southcombe, J. E. Chemistry of the Oil Industries. (Outlines of In¬ 


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Soxhlet, D. H. Dyeing and Staining Marble. Trans, by A. Morris and 

H. Robson.8vo, 

Spang, H. W. A Practical Treatise on Lightning Protection.nmo, 

Spangenburg, L. Fatigue of Metals. Translated by S. H. Shreve. 

(Science Series No. 23.).i6mo, 

Specht, G. J., Hardy, A. S., McMaster, J. B., and Walling. Topographical 

Surveying. (Science Series No. 72.).i6mo, 

Speyers, C. L. Text-book of Physical Chemistry.8vo, 

Sprague, E. H. Hydraulics.i2mo, 

Stahl, A. W. Transmission of Power. (Science Series No. 28.) . i6mo, 

Stahl, A. W., and Woods, A. T. Elementary Mechanism.i2mo, 

Staley, C., and Pierson, G. S. The Separate System of Sewerage.. .8vo, 

Standage, H. C. Leatherworkers’ Manual.8vo, 

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-Agglutinants of all Kinds for all Purposes.i2mo, 

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Stansbie, J. H. Iron and Steel. (Westminster Series.). 3 vo, 

Steadman, F. M. Unit Photography and Actinometry. (In Press.) 

Stecher, G. E. Cork. Its Origin and Industrial Uses.izmo, 

Steinman, D. B. Suspension Bridges and Cantilevers. (Science Series 

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Stevenson, J. L. Blast-Furnace Calculations.i2mo, leather, 

Stewart, A. Modern Polyphase Machinery.i2mo, 

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Stillman, P. Steam-engine Indicator.i2mo, 

Stodola, A. Steam Turbines. Trans, by L. C. Loewenstein.8vo, 

Stone, H. The Timbers of Commerce.8vo, 

Stone, Gen. R. New Roads and Road Laws.i2mo, 

Stopes, M. Ancient Plants.8vo, 

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Stumpf, Prof. Una-Flow of Steam Engine.4to, 

Sudborough, J. J., and James, T. C. Practical Organic Chemistry.. i2mo, 

Suffling, E. R. Treatise on the Art of Glass Painting.8vo, 

Swan, K. Patents, Designs and Trade Marks. (Westminster Series.). 

8vo, 

Swinburne, J., Wordingham, C. H., and Martin, T. C. Electric Currents. 

(Science Series No. 109.).i6mo, 

Swoope, C. W. Lessons in Practical Electricity.i2mo, 


*3 OP 

*2 50 
1 oo 

o 50 

o 50 
*2 25 
I 25 

*2 00 
*3 00 
*3 50 
*2 00 
*3 50 

*2 00 

1 00 

o 50 
*2 50 

*2 00 
*2 00 
*1 25 
1 00 
1 00 
*5 00 

3 5 o 
1 00 
*2 00 
*2 00 
*3 50 
*2 00 
*3 50 

*2 00 

o 50 
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Tate, J. S. Surcharged and Different Forms of Retaining-walls. (Science 

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i2mo, morocco, 


2 00 




































28 D. VAN NOSTRAND CO/S SHORT TITLE CATALOG 


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Terry, H. L. India Rubber and its Manufacture. (Westminster Series.) 

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Vol. II. Design of Simple Structures. {In Preparation.) 

Vol. III. Design of Advanced Structures. {In Preparation.) 

Thiess, J. B., and Joy, G. A. Toll Telephone Practice.8vo, 

Thom, C., and Jones, W. H. Telegraphic Connections., oblong, i2mo, 

Thomas, C. W. Paper-makers’ Handbook. {In Press.) 

Thompson, A. B. Oil Fields of Russia.4to, 

-Petroleum Mining and Oil Field Development.8vo, 

Thompson, S. P. Dynamo Electric Machines. (Science Series No. 75.) 

i6mo, 

Thompson, W. P. Handbook of Patent Law of All Countries.i6mo, 

Thomson, G. S. Milk and Cream Testing.i2mo, 

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Thornley, T. Cotton Combing Machines.8vo, 

-Cotton Waste..8vo, 

-Cotton Spinning. 8vo. 

First Year. 

Second Year. 

Third Year. 


Thurso, J. W. Modern Turbine Practice..8vo, 

Tidy, C. Meymott. Treatment of Sewage. (Science Series No. 94.)i6mo, 
Tillmans, J. Water Purification and Sewage Disposal. Trans, by 
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Tinney, W. H. Gold-mining Machinery.8vo, 

Titherley, A. W. Laboratory Course of Organic Chemistry.8vo, 

Toch, M. Chemistry and Technology of Mixed Paints.8vo, 

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{In . Press.) 

Tod, J., and McGibbon, W. C. Marine Engineers’ Board of Trade 


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Tonge, J. Coal. (Westminster Series.).8vo, 

Townsend, F. Alternating Current Engineering.8vo, boards, 

Townsend, J. Ionization of Gases by Collision.8vo, 


Transactions of the American Institute of Chemical Engineers, 8vo. 

Vol. I. 1908. 

Vol. II. 1909.... 

Vol. III. 1910. 

Vol. IV. 1911. 

Vol. V. 1912. 

Vol. VI. 1913. 


Traverse Tables. (Science Series No. 115.).i6mo, 

morocco, 

Treiber, E. Foundry Machinery. Trans, by C. Salter.i2mo, 


*2 oa 
*2 00 


*3 50 
1 50 

*7 50 
*5 00 

o 50 
1 50 
*1 75 
*3 00 
*3 00 
*3 00 

*1 50 
*2 50 
*2 50 
*4 00 
o 50 

*2 00 
*3 00 
*2 00 
*3 00 
*2 00 


*1 50 

*7 50 
*2 00 
*0 75 
*1 25 

*6 00 
*6 00 
*6 00 
*6 00 
*6 00 
*6 oa 

0 50 
1 00 
1 25 






































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29 

Trinks, W., and Housum, C. Shaft Governors. (Science Series No. 122.) 

i6mo, o 50 

Trowbridge, W. P. Turbine Wheels. (Science Series No. 44.). . i6mo, 0 50 

Tucker, J. H. A Manual of Sugar Analysis.8vo, 3 50 

Tunner, P. A. Treatise on Roll-turning. Trans, by J. B. Pearse. 

8vo, text and folio atlas, 10 00 

Turnbull, Jr., J., and Robinson, S. W. A Treatise on the Compound 

Steam-engine. (Science Series No. 8.).i6mo, 

Turrill, S. M. Elementary Course in Perspective.nmo, *1 25 

Underhill, C. R. Solenoids, Electromagnets and Electromagnetic Wind¬ 
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Underwood, N., and Sullivan, T. V. Chemistry and Technology of 

Printing Inks. (In Press.) 

Urquhart, J. W. Electric Light Fitting.i2mo, 200 

-Electro-plating.i2mo, 200 

-Electrotyping.i2mo, 2 00 

-Electric Ship Lighting.12010, 3 00 

Usborne, P. O. G. Design of Simple Steel Bridges.8vo, *4 00 

Vacher, F. Food Inspector’s Handbook. 

Van Nostrand’s Chemical Annual. Third issue 1913... .leather, 12010, *2 5© 

-Year Book of Mechanical Engineering Data. (In Press.) 

Van Wagenen, T. F. Manual of Hydraulic Mining.i6mo, 1 00 

Vega, Baron Von. Logarithmic Tables.8vo, cloth, 200 

half morroco, 2 50 

Vincent, C. Ammonia and its Compounds. Trans, by M. J. Salter. 8vo, *2 00 

Volk, C. Haulage and Winding Appliances.8vo, *400 

Von Georgievics, G. Chemical Technology of Textile Fibres. Trans. 

by C. Salter. 8vo, *4 5o 

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V©se, G. L. Graphic Method for Solving Certain Questions in Arithmetic 

and Algebra (Science Series No. 16.).i6mo, o 50 

Vosmaer, A. Ozone. (In Press.) 

Wabner, R. Ventilation in Mines. Trans, by C. Salter.8vo, *4 50 

Wade, E. J. Secondary Batteries.8vo, *4 00 

Wadmore, T. M. Elementary Chemical Theory.12010, *150 

Wadsworth, C.. Primary Battery Ignition.12010, *050 

Wagner, E. Preserving Fruits, Vegetables, and Meat.12010, *250 

Waldram, P. J. Principles of Structural Mechanics.12010, *300 

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